There's also the complication that, by their own logic, "the right to X of your gender identity" is effectively "the right to X of your choice", because gender identity is distinct from gender expression.

Even TRAs have to concede that verbal declarations of gender are part of the latter. They even use the term "chosen gender" in the context of public policy.

Any clinical recognition of gender is a joke, as TRAs consistently push to lower the bar for a gender dysphoria diagnosis (when they're not outright saying you don't need to have dysphoria to be trans) and we've seen plenty of troons advising other troons to lie to their doctors.

As long as gender identity remains an unfalsifiable quasi-spiritual Gnosis, the category of people TRAs think are women (anyone who identifies "in good faith" as a woman) is not the category of people TRAs think are entitled to women's spaces (anyone who decides to use the English word "woman" to describe themself at that moment), so these are two separate issues.

You can agree that trans women are women (as J. K. Rowling once did) and still defend sex-segregated spaces, or vice versa.

But if TRAs addressed these issues separately, they wouldn't be able to fall back on thought-terminating cliches like "my existence is not up for debate!!" when arguing for replacing sex-segregated spaces with verbal-declaration-segregated spaces.

If they completely detach the "essence" of womanhood from any reality outside their own minds, be it natural or social reality (or even the wildly varying meanings of womanhood inside other TRA's minds), they detach it from the social standard of woman-only spaces, they can't have it both ways.