This probably doesn't generalize beyond very niche subcultures, but in the one I'm a member of, the Furry Fandom, art drawn by real artists is such a core aspect that, even though furries use generative AI for fun, we don't value it. One reason behind this is that, different from more typical fandoms, in which members are fans of something specific made by a 3rd party, in the Furry Fandom members are fans of each other.

Give that, and assuming the Furry Fandom continues existing in the future, I expect members will continue commissioning art from each other or, at the very least, will continue wanting to be able to commission art from each other, and will use AI-generated art as a temporary stand in while they save to commission real pieces from the actual artists they admire.

There has been a lot of useful discussion in the answers and comments, which has caused me to revise and expand parts of my list. So that readers looking for practical career advice don't have to read the entire comments section to find the actual resulting advice, it seemed useful to me to give a revised list. Doing this as an answer in the context of this question seems better than either making it a whole new post, or editing the list in the original post in a way that would remove the original context of the answers and comments discussion.

This is my personal attempt to summarize the answers and comments discussion: other commenters may not agree (and are of course welcome to add comments saying so). As the discussion continues and changes my opinion, I will keep this version of the list up to date (even if that requires destroying the context of any comments on it).

List of Job Categories Safe from AI/Robots (Revised)

1. Doing something that machines can do better, but that people are still willing to pay to watch a very talented/skilled human do about as well as any human can (on TV or in person).

   Examples: chess master, Twitch streamer, professional athlete, Cirque du Soleil performer.

   Epistemic status: already proven for some of these, the first two are things that machines have already been able to do better than a human for a while, but people are still interested in paying to watch a human do them very well for a human. Also seems very plausible for the others that current robotics is not yet up to doing better.

   Economic limits: If you're not in the top O(1000) people in the world at some specific activity that plenty of people in the world are interested in watching, then you can make roughly no money off this. Despite the aspirations of a great many teenaged boys, being an unusually good (but not amazing) video gamer is not a skill that will make you any money at all.

2. Doing some intellectual and/or physical work that AI/robots can now do better, but for some reason people are willing to pay at least an order of magnitude more to have it done less well by a human, perhaps because they trust humans better. This could include jobs where people's willingness to pay is due to a legal requirement that certain work be done or supervised by a (suitably skilled/accredited) human (and these requirements have not yet been repealed).

   Examples: Doctor, veterinarian, lawyer, priest, babysitter, nanny, nurse, primary school teacher.

   Epistemic status: Many people tell me "I'd never let an AI/a robot do <high-stakes intellectual or physical work> for me/my family/my pets…" They are clearly quite genuine in this opinion, but it's unclear how deeply they have considered the matter. It remains to be seen how long this opinion will last in the presence of a very large price differential when the AI/robot-produced work is actually, demonstrably, just as good if not better.

   Economic limits: I suspect there will be a lot of demand for this at first, and that it will decrease over time, perhaps even quite rapidly (though perhaps slower for some such jobs than others). Requires being reliably good at the job, and at appearing reassuringly competent while doing so.

3. Giving human feedback/input/supervision to/of AI/robotic work/models/training data, in order to improve, check, or confirm its quality.

   Examples: current AI training crowd-workers, wikipedian (currently unpaid), acting as a manager or technical lead to a team of AI white collar workers, focus group participant, filling out endless surveys on the fine points of Human Values

   Epistemic status: seems inevitable, at least at first.

   Economic limits: I imagine there will be a lot of demand for this at first, I'm rather unsure if that demand will gradually decline, as the AIs get better at doing things/self-training without needing human input, or if it will increase over time because the overall economy is growing so fast and/or more capable models need more training data and/or society keeps moving out-of-previous distribution so new data is needed. [A lot of training data is needed, more training data is always better, and the resulting models can be used a great many times, however there is clearly an element of diminishing returns on this as more data is accumulated, and we're already getting increasingly good at generating synthetic training data.] Another question is whether a lot of very smart AIs can extract a lot of this sort of data from humans without needing their explicit paid cooperation — indeed, perhaps granting permission for them to do so and not intentionally sabotaging this might even become a condition for part of UBI (at which point deciding whether to call allowing this a career or not is a bit unclear).

4. Skilled participant in an activity that heavily involves interactions between people, where humans prefer to do this with other real humans, are willing to pay a significant premium to do so, and you are sufficiently more skilled/talented/capable/willing to cater to others' demands than the average participant that you can make a net profit off this exchange.

   Examples: director/producer/lead performer for amateur/hobby theater, skilled comedy-improv partner, human sex-worker

   Epistemic status: seems extremely plausible

   Economic limits: Net earning potential may be limited, depending on just how much better/more desirable you are as a fellow participant than typical people into this activity, and on the extent to which this can be leveraged in a one-producer-to-many-customers way — however, making the latter factor high is is challenging because it conflicts with the human-to-real-human interaction requirement that allows you to out-compete an AI/robot in the first place. Often a case of turning a hobby into a career. 

5. Providing some nominal economic value while being a status symbol, where the primary point is to demonstrate that the employer has so much money they can waste some of it on employing a real human ("They actually have a human maid!")

   This can either be full-time employment as a status-symbol for a specific status-signaler, or you can be making high-status "luxury" goods where owning one is a status signal, or at least has cachet. For the latter, like any luxury good, they need to be rare: this could be that they are individually hand made, and-or were specifically commissioned by a specific owner, or that they are reproduced only in a "limited edition".

   Examples: (status symbol) receptionist, maid, personal assistant; (status-symbol maker) "High Art" artist, Etsy craftsperson, portrait or commissions artist, mechanical watch hand-assembler.

   Epistemic status: human nature (for the full-time version, assuming there are still people this unusually rich).

   Economic limits: For the full-time-employment version, there are likely to be relatively few positions of this type, at most a few per person so unusually rich that they feel a need to show this fact off. (Human nobility used to do a lot of this, centuries back, but there the servants were supplying real, significant economic value, and the being-a-status-symbol component of it was mostly confined to the uniforms the servant swore while doing so.) Requires rather specific talents, including looking glamorous and expensive, and probably also being exceptionally good at your nominal job.

   For the "maker of limited edition human-made goods" version: pretty widely applicable, and can provide a wide range of income levels depending on how skilled you are and how prestigious your personal brand is. Can be a case of turning a hobby into a career.

6. Providing human-species-specific reproductive or medical services.

   Examples: Surrogate motherhood, wet-nurse, sperm/egg donor, blood donor, organ donor.

   Epistemic status: still needed.

   Economic limits: Significant medical consequences, low demand, improvements in medicine may reduce demand.

Certain jobs could manage to combine two (or more) of these categories. Arguably categories 1. and 5. are subsets of category 2.

Note also that for categories 1, 4, 5, and 6, the only likely customer base is other humans: so if all other humans are impoverished, these will not help you not be impoverished. 3 on the other hand is providing value to the AI portion of the economy, and 2 might (especially in the regulatory capture variant of it) sometimes have part of the AI portion of the economy as a customer. So how long jobs in category 3, and the "legally required" variant of 2, continue to exist for is rather key for how money flows between the AI and human portions of the economy. Modeled as two separate trading blocks, then ignoring any taxation/redistribution, the AI economy has a great deal to offer the humans (goods, services, entertainment, knowledge), while all the humans have to offer are 2 (if legally required) and 3.

The recent Carl Shulman podcast (part 1, part 2) is informative on this question (though it should be taken in the spirit of exploratory engineering, not forecasting). In particular, in a post-AGI magically-normal world, jobs that humans are uniquely qualified to do won't be important to the industry and will be worked around. What remains of them will have the character of billionaires hiring other billionaires as waiters, so treating this question as being about careers seems noncentral.

I think my answer would depend on your answer to "Why do you want a job?". I think that when AI and robotics have advanced to the point where all physical and intellectual tasks can be done better by AI/robots, we've reached a situation where things change very rapidly and "what is a safe line of work long term?" is hard to answer because we could see rapid changes over a period of a few years, and who knows what the end-state will look like? Also, any line of work which at time X it is economically valuable to have humans do, will have a lot of built-in incentive to make it automateable, so "what is it humans can make money at because people value the labour?" could change rapidly. For example, you suggest that sex work is one possibility, but if you have 100,000 genius-level AIs devising the best possible sex-robot, pretty quickly they'd be able to come up with something where the people who are currently paying for sex would feel like they're getting better value for money out of the sex-robot than out of a human they could pay for sex. Of course people will still want to have sex with people they like who like them back, but that isn't typically done for money.

We'll live in a world where the economy is much larger and people are much richer, so subsistence isn't a concern, provided that there's decent redistributive mechanisms of some sort in place. Like let's say we keep the tax rate the same but the GDP has gone up 1,000x - then the amount of tax revenue has gone up 1,000x, and UBI is easy. If we can't coordinate to get a UBI in place, it would still only need 1 in 1,000 people to somehow have lucked into resources and say "I wish everyone had a decent standard of living" and they could set up a charitable organization that gave out free food and shelter, with the resources under their command. So you won't need a job. Meaning, any work people got other people to do for them would have to pay an awful lot if it was something a worker didn't intrinsically want to do (if someone wanted a ditch dug for them by humans who didn't like digging ditches, they'd have to make those humans a financial offer they found made it worthwhile when all of their needs are already met - how much would you have to pay a billionaire to dig you a ditch? There's a price, but it's probably a lot.), and otherwise, you can just do whatever "productive" thing you want because you want to, you enjoy the challenge, it's a growth experience for you or whatever, and it likely pays 0, but that doesn't matter because you value it for reasons other than the pay.

I guess it could feel like a status or dignity thing, to know that other people value the things you can do, enough to keep you alive with the products of your own labour? And so you're like "nah, I don't want the UBI, I want to earn my living". In that case, keep in mind "enough to keep you alive with the products of your own labour" will be very little, as a percentage of people's income. So you can busk on a street corner, and people can occasionally throw the equivalent of a few hundred thousand of today's dollars of purchasing power into your hat, because you made a noise they liked, in the same way that I can put $5 down for a busker now because that amount of money isn't particularly significant to me, and you're set for a few years at least, instead of being able to get yourself a cup of coffee as is the case now.

Or, do you want to make a significant amount of money, such that you can do things most people can't do because you have more money than them? In that case, I think you'd need to be pushing the frontier somehow - maybe investing (with AI guidance, or not) instead of spending in non-investy ways would do it. If the economy is doubling every few years, and you decide to live on a small percentage of your available funds and invest the rest, that should compound to a huge sum within a short time, sufficient for you to, I dunno, play a key role in building the first example of whatever new technology the AI has invented recently which you think is neat, and get into the history books?

Or do you just want to do something that other people value? There will be plenty of opportunities to do that. When you're not constrained by a need to do something to survive, you could, if you wanted, make it your goal to give your friends really good and thoughtful gifts - do things for them that they really appreciate, which yes they could probably train an AI agent to do, but it's nice that you care enough to do that, the fact that you put in the thought and effort matters. And so your relationships with them are strengthened, and they appreciate you, and you feel good about your efforts, and that's your life.

Of course, there are a lot of problems in the world that won't magically get fixed overnight even if we create genius-level AIs and highly dexterous robots and for whatever reason that transition causes 0 unexpected problems. Making it so that everybody's life, worldwide, is at least OK, and we don't cause a bunch of nonhuman animal suffering, is a heavy lift to do from where we are, even with AI assistance. So if your goal is to make the lives of the people around you better, it'll be a while before you have a real struggle to find a problem worth solving because everything worthwhile has already been done, I'd think. If everything goes very well, we might get there in the natural un-extended lifetimes of people alive today, but there will be work to do for at least a decade or two even in the best case that doesn't involve a total loss of human control over the future, I'd think. The only way all problems get solved in the short term and you're really stuck for something worthwhile to do, involves a loss of human control over the situation, and that loss of control somehow going well instead of very badly.

For arbitrary time horizons nothing is 'safe', but that just means our economy shifts to a new model. It doesn't mean the outcome is bad for humans. I don't know if it makes sense to worry about which part of the ship will become submerged first because everyone will rush for the other parts and those jobs will be too competitive. It might be better to worry about how to pressure the political system to take proactive action to rearchitect our economy. Ubi and/or a shorter workweek are inevitable and the sooner we sort out how to implement that the better.

for the sake of understanding the roadmap for the autopocalypse, I think you can consider these factors:

The most obvious: can the work be entirely computer-based? A corollary to this is whether a unskilled human with the assistance of an ai can replace the skilled human (e.g. Healthcare roles requiring knowledge work and physical work)

Regulatory environment. Even if it were possible for software to replace a human worker licensing requirements and other laws may protect human workers for awhile beyond that point.

Eventually machines will be able to transcend software to perform every physical task a human can now perform. And that mostly won't be anthropomorphic robots but more automation of machines that currently are operated by humans, like cars and drones. The anthropomorphic robots will appear (on the job) the furthest into the future.

But again everyone will be racing away from these jobs (and toward the remaining 'safe' ones) at the same time. Financial investment may be the safest source of income. Owning your own business may possibly benefit from the autopocalypse but at the extreme you will just be an investor in a company run by machines.

TLDR:

So the best advice is probably to build an investment portfolio (and the knowledge to do that well). If you own the companies it doesn't matter who the workers are.

I have another category.

Probably the last human sense that we will give robots an accurate version of is scent (and the large proportion of the sense of taste that is actually scent). Not least because human scent is both a very complex sense and actively varies between individuals. Reading a gas chromatography output is not the same thing. There are jobs like perfumier, chef, and oenologist/sommelier where having a detailed sense of smell and predicting how humans will emotionally react to a specific scent/taste is inherent to the job: using scent/taste as an artform. These jobs should be especially resistant to automation. But there aren't a vast number of them, and their outputs can then be mass produced: if a chef comes up with a recipe, robots sufficiently competent in the kitchen can replicate cooking it. And automating "add salt to taste" or "check the spiciness level of the peppers" probably is possible, without duplicating the entire sense of taste.

You missed what I think would be by far the largest category, regulatory capture: jobs where the law specifically requires a human to do a particular task, even if it's just putting a stamp of approval on an AI's work. There are already a lot of these, but it seems like it would be a good idea to create even more, and add rate limits to existing ones.