Yes, again, I agree. It absolutely has become a "culture war litmus test". But that's because there's been this push to redefine "woman" in a way that takes it from 99+% accuracy to almost meaningless. The definition that seems to be most popular in postmodernist circles is "anybody who identifies as a woman." But as I'm sure you see, the circularity of this definition renders it useless.
I think you do a great job of challenging postmodernist philosophy which is why I find this confusing. I guess what I'm trying to understand is why the definition of woman needs to include trans women. What's the problem with the term trans woman? Which is uncontroversial, well understood, and leaves us all room to discuss more pressing issues for trans people.