I agree with a lot of your points here but I think you (and Timpf) are underselling many of the motivations underlying the culture wars. This isn't just about superficial status posturing, popularity contests, and meaningless culture war idiocies that are stoked by our political leaders (although those elements are often present too). There are actual, tangible, real world, harmful effects occurring because of so many of these ideas and attitudes, and combatting those effects is important.
When parent get upset about gender ideology being taught in schools it's not just because politicians inflamed the discourse. It's because they are justifiably concerned about how it will influence their kids.
When campaigns are waged against affirmative action in universities, it's not just because the campaigners want to stoke racial grievances, but because they can point to actual groups being discriminated against.
When average citizens speak out against CRT, it's not just because they're worked up over another culture war battle that our leaders want to score points over, but because they recognize the divisions and grievances it is sowing in society.
I'm all for people trying to look past our differences and for us all to disagree more civilly, but I don't think we should downplay the fundamental issues that are at the core of why we are arguing so much. There are some very toxic and harmful ideas that are being taught, spread, and promoted, and we should not be papering them over as if they are of no more significance than the latest fashion trend.