Subject: Re: Can't They Just Leave Women Alone?
My point was that they would have to document it, which implies legal proceedings, which cost the trans-person money.

I don't think that implication is sound. It's not going to get to legal proceedings except when the person is faking. If the cops get called, they'll just ask a few people that know the person in question - "Does this person really go by their new trans name? Do they act in a way consistent with being a woman outside the gym locker?" - etc. They might ask the person if they are seeing a therapist or counselor who can confirm that they've been diagnosed with gender dysphoria. Etc.

A trans person will be able to resolve that quickly and easily. A cis person who's just trying to see naked people will not.