Watson

Well if you don't have a binary on biology, getting a defined idea of woman by belief is surely impossible. What is a woman?

We don't even have a binary on the biological definitions of "alive" and "dead," yet we understand the concepts well enough to use them, don't we? Making sure the definition of a word is simple and universal just isn't that important to the word having meaning.

So what is a woman?

For the purpose of communicating to other people, "adult human who identifies as a woman" or "adult human who agrees with others identifying her as a woman" works fine. It's a very socially contingent sort of word.

This sounds an awful lot like "I have no problem with gay people getting civil partnerships and calling themselves married, but the DEFINITION OF MARRIAGE doesn't need to change!!!!"

Like, this isn't that complicated. Trans women are adult human females too. Just be slightly less uptight about everything needing a cast-iron tightly-bounded definition with no exceptions or irregularities.