I live in the United States, specifically the San Francisco Bay Area, which is known for queer culture and acceptance of different people.
I regularly use the bathroom and locker rooms with trans women, and have so for years. It’s never been a problem.
At my former job, there was a nearby office with a trans woman and I ran into her regularly in the bathroom. It was fine, she acted like anyone else did in a bathroom.
At my martial arts school there have been a number of trans women at the school who used the women’s changing room with me. Again it was fine. At no time did they do anything weird or act like men at all.
At my old gym there were a couple trans women members who showered and used the women’s locker room. I even spent time in a sauna with one once. We were both just wearing towels. It was literally the same as hanging out with any other woman.
I wonder of many of these women who fear trans women invading their spaces have actually tried using the bathroom or sharing a locker room with a trans woman. I wonder if most of them even know any trans women. Because for me, there was never anything weird there. Yes, some trans women have penises (some are also post-opp) but it’s not like they are swinging their dicks around demanding we all look at them. None of the women I have interacted with did I ever catch a glimpse of their member, nor was I trying to look at it. Generally they are quite discrete about it and we don’t go starring at each other. Most of them were quite meek and were trying not get beat up in the locker room for being trans.
I know the idea of sharing a female only space can be quite scary, I see how the idea freaks people out. But my experience with trans women is that in practice or wasn’t scary at all. They acted like women using the bathroom, not like men proud of their genitalia and trying to gain power over us. So it’s the sort of thing that in theory may feel intimating but in practice it feels just like sharing space with another female.
At my job, there is a single use bathroom that is reserved for people who feel uncomfortable using a the binary gender bathrooms. I work at a school and a number of my students are trans and non-binary. I think providing a unisex bathroom is a better option to deal with people who don’t feel comfortable sharing bathrooms with trans women or anyone else for that matter. I think that would be a better accommodation than forcing trans women to use the bathroom with men. JKR often talks about trans women as if they are men, and to be clear I don’t want to share a bathroom with men either. I wouldn’t want one the bathroom with me. But trans women aren’t men, and it feels little like some people think they are and don’t want them in the bathroom because of that.