I will speak on this changing room issue specifically.
There are a lot of the pro trans lobby, and here I am speaking about Natal women particularly, who seem not to like men very much and fear them a lot. While claiming to be progressive in many instances, they have double standards when it comes to prejudice towards men: racism, body shaming, all the things you see them talk out about most avidly and lecture others who they think aren't progressive enough.
Part of their progressive politics is lobbying for trans people to have full access to changing rooms and use them the same way natal women use them.
Let me tell you about how natal women use my local changing room. They walk around butt naked for IMO, far longer than necessary. There are cubicles and there are ways where you can limit the duration of your nudity. Again IMO, these are steps we should be taking in public changing rooms.
Lots of these women are the same women who seem to simultaneously find natal men (and their bodies) quite repulsive and lobby for trans women to be able to use female changing rooms like they do.
If we did get to a place where everyone accepted a law where it became totally normal to see trans women naked in changing rooms, I don't think those natal women would be as okay with it as they think they will. I think they imagine trans women using their changing rooms, but hiding themselves. It isnt dissimilar to how they treat Black women when they want to take equal space somewhere that is designated for all women.