A lot of people care about the culture wars because they don't believe the singularity is coming soon. Yet a lot of people who do believe it is coming soon still seem just as invested (e.g. Elon Musk, Peter Thiel, and others on the left wing).

Why?

Because the results of culture wars now will determine the post-singularity culture.

As you repeatedly point out, there are multiple solutions to each issue. Assuming good enough technology, all of them are viable. Which (if any) solutions end up being illegal, incentivized, made fun of, or made mandatory, becomes a matter of which values end up being normative. Thus, these people may be culture-warring because they think they're influencing "post-singularity" values. This would betray the fact that they aren't really thinking in classical singularitarian terms.

Alternatively, they just spent too much time on twitter and got caught up in dumb tribal instincts. Happens to the best of us.

Because people aren't rational. Motivated reasoning is a big factor but also we're all trying to think using monkey brains.

Believing what feels good is evolutionarily adaptive in the sense arriving at correct conclusions about whether God or Singularities exist won't help much if it makes your tribesmates dislike you. This bias is a cumulative, recursive problem that stacks up over the thousands or millions of cognitive acts that go into our beliefs about what we should care about.

And this gets a lot worse when it's combined with our sharp cognitive limitations. We seem to have roughly the least cognitive capacity that still lets a species as a whole very slowly invent and build technologies.

We are idiots, every last one of us. Rationalists with tons of knowledge are a bit less idiotic, but let's don't get cocky - we're still monkey-brained idiots. We just don't have the cognitive horsepower to do the Bayesian math on all the relevant evidence, because important topics are complex. And we're resistant but far from immune to motivated reasoning: you've got to really love rationalism to enjoy being proven wrong and so not turning away cognitively it when it happens.

What I take from all this is that humans are nobly struggling against our own cognitive limitations. We should try harder in the face of rationality being challenging. Success is possible, just not easy and never certain. And very few people are really bad; they're just deluded.

To your exact question:

Musk believes in an intelligence explosion. He cares a lot about the culture war because, roughly as he puts it, he's addicted to drama. I don't know about Thiel.

Most of humanity does not believe in an intelligence explosion happening soon. So actually people who both believe in a singularity and still care about culture wars are quite rare.

I do wonder why people downvoted this quite reasonable question. I suspect they're well-meaning monkey-brained idiots, just like the rest of us.

To add to the other answers, outside of the induced consequences post-singularity, what happens pre-singularity still matters if the singularity does not happen extremely soon.

1. we don't know when (or IF!) the singularity will happen
2. does nothing matter until then? What if the singularity happens in a century? Should you abandon all your beliefs because one day when you'll be (likely) dead, people will have solved all problems?

The culture wars can have an impact on (1) how fast we get to the Singularity and whether we survive it, and (2) what rules will the superintelligences follow afterwards.

If the culture warriors decide that STEM is evil, and that instead of math we should teach wokeness during the math lessons, it could have a negative impact on math education, with downstream effects on people who will build the AIs and try to make them safe.

The culture warriors may achieve encoding various political taboos to the AIs. If the future is decided by those AIs, it might mean that the taboos will remain in effect literally until the heat death of the universe.

Consider the current taboo on anything sexual. Now imagine that 10 years later, the AIs built with these taboos may literally control the world. Will people be allowed to have sex (or even masturbate)? This may sound silly, but at which moment and by what mechanism will the AIs decide that the old rules no longer apply? Especially if we want other rules, such as not hurting people, to remain unchanged forever.

A part of politics is hating your enemies. What will happen to those political enemies after Singularity -- will they be forgiven and allowed to enter the paradise as equals, or will they have to atone for their sins (e.g. being born white and male) literally forever?

When the technology makes it possible to literally edit other people's minds, I suppose it will be quite tempting for the winning political coalition to forcibly edit everyone's minds according to their values. It will start with "let's eradicate racism", and then the definition of unacceptable intolerance will keep expanding, until you are not allowed to keep any of your original beliefs (that someone might feel offended by) or sexual preferences (that someone might feel excluded by). Everyone will be mind-raped in the name of the greater good (we do not negotiate with Nazis).

Oh, someone might even decide that the desire to be immortal is just some stupid white patriarchal colonialist value or something, and we should instead embrace some tribal wisdom explaining why death is good or something.

We need to decide how much controls parents will have over their kids. These days, at least the abuse is illegal, and kids are allowed to leave their homes at 18 (and this part would become trivial after Singularity). But what if your parents are legally allowed to edit your brain, and e.g. make you want to remain perfectly loyal to them no matter what? What if your parents want to make you so deeply religious that you will want to commit to rather die than doubt your faith (and the AI will respect your commitments)? Or will it be the other way round, and the AI will take your children away if it notices that you are teaching them something politically incorrect?

Uhm, will people be allowed to reproduce exponentially? It may turn out that even the entire universe it literally not large enough. If people are not allowed to reproduce exponentially, who decides how many children they can have? Will there be racial quotas to prevent some ethnic groups from out-reproducing others? Will there be a ban on religious conversion, because it would modify the balance between religious groups? By the way, in some faiths, birth control is a sin; will the AIs enforce this sin?

Privacy -- will people be allowed to have any? Freedom of association -- is it okay for a group of people to meet privately and never tell anyone else what happens there? Or does the curiosity of many matter more than the privacy of a few?

A fourth or fifth possibility: they don't actually alieve that the singularity is coming