I’m going to mentally swap out “males” for “trans women”, since that’s what you really meant when you tried to re-enforce the false idea that trans women are men.

Yes, they are bigots when there’s no justifiable reason. I’ve already posted the study showing that whether you allow trans women in or not makes no difference to women’s safety. So, as I have said (though you didn’t read because you’re scared of your opinion being wrong), if you accept a limitation of privacy from cis women you have to accept the same limitation of privacy from trans women, otherwise you are just being prejudiced.

Deal with it, I guess?