What a bizarre thing to say! Recognising that there's a difference between a transvestite and a transgender person and expecting that the question of whether they should have legal access to women's spaces is not an excuse for inaction but an attempt not to take action that harms women.
I am constantly astonished by how little empathy people have for the privacy and comfort of women on this issue. You respect "personal gender" but are happy to take a "move fast and break things" approach to women's rights and safety. What could possibly go wrong?
Also, "rape is often used as a divisive and inflammatory talking point." Are you high?! It's not a talking point. It's a thing that happens. Primarily to women. I have no idea what point you think you're making there. I actulally included a trigger warning regarding rape on a recent article. I didn't (and still don't) think it necessary for a single mention of it.
Getting offended on behalf of other, hypothetical people must be so tiresome, no?