Edge cases don't invalidate the general usefulness of abstracting messy collections of correlated observations into a single category. But they do strongly suggest that whatever rule of thumb you're using to categorize is a statistical heuristic, and not an objective criteria, because it fails in some cases. Put another way, it is correct to say that humans have 10 fingers, even though some humans have 9 fingers. But it would be incorrect to say that 9 fingered people are inhuman, because having 10 fingers is a general observed phenomenon and not an actual criteria that you need to meet to be human.

Take biological sex. Humans are sexually differentiated across almost every facet of our biology. Any intersex individual doesn't invalidate that. You can say that males are XY and females are XX and be right in the vast majority of cases. But if you're the medical doctor of an XY patient with Swyer's syndrome, you need to be able to understand that they still have female estrogen levels from hormone therapy, have developed female breasts, and so need breast cancer screening even though their genotype is male. In rare cases they may even be pregnant. At the individual level the broad categorizations of "female" and "male" aren't always useful or accurate, and you need to dig into the actual individual facts the categories are abstracting away. There is no one measurable criteria that is going to be always correct on defining category membership on the individual level, because a category is a statistical grouping, not an objective property in and of itself.

One option might be 'do the rationalist-ish thing when you're forced to because it's decision-relevant; but when you're just analyzing an interesting intellectual puzzle for fun, don't do the rationalist-ish thing'

This is the closest to what I was trying to say, but I would scope my criticism even more narrowly. To try and put it bluntly and briefly: Don't choose to suspend disbelief for multiple core hypotheses within your argument, while simultaneously holding that the final conclusion built off of them is objectively likely and has been supported throughout. 

The motte with this argument style, that your conclusion is the best you can do given your limited data, is true and I agree. Because of that this is a genuinely good technique for decision making in a limited space, as you mention. What I see as the bailey though, that your conclusion is actually probable in a real and objective sense, and that you've proven it to be so with supporting logic and data, is what doesn't follow to me. Because you haven't falsified anything in an objective sense, there is no guaranteed probability or likelihood that you are correct, and you are more likely to be incorrect the more times in your argument you've chosen to deliberately suspend disbelief for one of your hypotheses to carry onward. Confidence intervals are a number you're applying to your own feelings, not actual odds of correctness, so can't be objectively used to calculate your chance of being right overall.

Put another way, in science it is totally possible and reasonable for a researcher to have an informed hypothesis that multiple hypothetical mechanisms in the world all exist, and that they combine together to cause some broader behavior that so far has been unexplained. But if this researcher were to jump to asserting that the broader behavior is probably happening because of all these hypothetical mechanisms, without first actively validating all the individual hypotheses with falsifiable experiments, we'd label their proposed broad system of belief as a pseudoscience. The pseudoscience label would still be true even if their final conclusion turned out to be accurate, because the problem here is with the form (assuming multiple mechanisms are real without validating them) rather than the content (the mechanisms themselves). This becomes better or worse the more of these hypothetical but unproven mechanisms need to exist and depend on each other for the researcher's final conclusion to be true.

I hear you on examples, but since I don't like posts that do this I don't have any saved to point at unfortunately. I can go looking for new ones that do this if you think it would still be helpful though.

The implied claim that I took from the passage (perhaps incorrectly) is that motte and bailey is a fallacy inherent to post-modernist thought in general, rather than a bad rhetorical technique that some post-modernists commenters engage in on the internet. From that it should be easier, not harder, to cite real-world examples of it since the rhetorical fallacy is actually widespread and representative of post-modern thought. The government example isn't analogous, as it would have at least been a real-world example and the person in that hypothetical wouldn't be trying to argue that the dysfunctional dynamic is inherent to all government. But the quote chose to make up an absurd post-modernist claim about the sun being socially constructed to try and prove a claim that post-modernism is absurd.

I made my aside because I am a relatively everyday person who is a general fan of post-modernism, or at least the concept of social construction as I've described, and I have a strong suspicion that whatever specific real-world examples the author is pattern-matching as denying objective reality probably have a stronger argument for being a socially constructed than they're aware of. Or at least able to hand-wave as absurd as easily as their sun hypothetical.

This is all just an aside of an aside though, and I somewhat regret putting it in the body of my post and distracting from the rest. People generally do make terrible arguments on the internet, so in terms of sheer volume I do agree that bad arguments abound.