I have an antidote for you. I knew a trans woman who used the mens bathroom for as long as possible. Then a man tried to rape her while she was in there.
Should she just go and be raped now in the future? Does being trans now mean it's okay to be victims of rape?
Here's is more anecdotal for you. I use public bathrooms with trans women regularly. Where I live, it's considered normal, and I have encountered more trans women in the bathroom than I can count. They have never acted like men there. They have never been rude, or creepy to me. In fact, trans women have been using women's bathrooms for over 50 years in most places. People only started caring due to the trans panic.
Trans women literally used the women's restroom in the 1950's, and there haven't been a whole lot of rape charges.
Trans women act like women in the bathrooms. They don't deserve to be raped anymore than any cis women.