Then maybe trans activism has been taken the wrong approach to meet the needs, or at least the comfort, of most trans people.

Sometimes, if a well-intentioned approach is having sufficiently unpleasant side-effects, it's a good idea to step back and ask, "Where did we go wrong?"

If the answer is, "we didn't realize that approximately half the human race consists of vile monsters", one hasn't stepped back far enough. One must keep going until most people seem like people. Then you can figure out how to work with them.

Of course, it is possible to end up the target of a moral panic without playing any role in it at all--the D&D panic of the 80s was a good example of this. But I don't think an honest reading of the situation with trans rights advocacy bears out that this has been the case.

I worry that trans advocates have decided too much to treat it like a war, complete with civilian casualties and friendly fire; I worry that trans people--including those I know--will feel caught in the crossfire, and even if not, that the battle will render many areas enemy territory where previously it would only have been moderately uncomfortable territory. I think you've completely glossed over this meta-narrative behind the existence of the Peterson-Joyce discussion.

I agree that a good deal of the debate was problematic in various ways. But I don't think that you fully rose to Chris's challenge to understand the other perspective, though it is a commendable attempt (and better than I've seen from nearly anyone who espouses an actually anti-trans position).

A few points you raise have relatively brief explanations:

(1) Critical Theory is Marxism-friendly (Marxism-inspired, even), and later Critical Theory took a decidedly post-modernist turn (though even Horkheimer lays all the foundation one needs), so it's not true that Marxism and post-modernism are necessarily at odds even though there is considerable tension. Additionally, both are popular among the far left, so you tend to get a hodgepodge of both proposed from among the same crowd that tends to be most vocally supportive of trans rights, even if it's not always the same people advocating for Marxism and taking a postmodern perspective.

(2) Linguistic battles are especially vitriolic because you cannot settle disputes by having both sides defer to reality. Your choices, if you're in a hurry, are to induce empathy, or to browbeat people with vitriol. (In the long run, you can just try to establish gradual adoption of the new terms.) I, too, doubt that this really is fully a linguistic battle, but if it were completely a linguistic battle, one would not be surprised that vitriol would feature prominently.

(3) There is no contradiction whatsoever in admitting that there is some degree of plasticity and some degree of biological determinism. Indeed, anything else is drastically at odds with evidence. So it's completely unjustified to ding Joyce for this. (There are plenty of other justified criticisms--just this one isn't.)