Where we differ is that, when it comes to the law, it's gender that counts.

You must have not read my piece. Trans women ARE women. One type of women. What matters is the legal definition, which goes by gender, not sex.

It would be quite jarring for men, and quite dangerous for me, as a woman, to go into male spaces.

The notion of the predatory monster trans woman is a fiction invented by conservatives to demonize us. There is no epidemic of trans women attacks in women's spaces. (There is plenty of evidence of republican senators sexually assaulting women.)

I am a trans woman. I am a woman. I use the female restroom, along with other women (cisgender or transgender). We sometimes gossip and laugh at jokes from adjacent stalls. I use the female changing room at the gym, and the other women at the gym have no objection to me being there. We gossip, we talk about our kids. (the ridiculous notion that I would expose my genitals is fiction, as is the notion that I'd be there to stare— hardly any woman walks nude across a changing room ever.
All of this is being looked at though a male lens, and it's unsettling how sure men are that everyone is a predator.
Quite telling, too.