Thanks for responding!
No, I can't look inside someone's head and tell you whether they're genuinely transgender or lying. Neither can you.
Oh, that's unfortunate. So when you said "Being transgender isn't about believing women wear dresses or act a certain way; it's about a person's gender identity" did you mean that we just need to guess, or take it on faith, that the man coming into a female single-sex space is not a man, but is actually a woman? Even though they might look exacty like a real man? How do we know?
But here's the question people in this group seem to be ignoring do you honestly believe a man intent on assaulting a woman is going to stop because a sign on a toilet door says "Women"?
Well, that's tricky, isn't it, because you just said we can't tell if a man is trans-identified or not. So how can we say if THIS man (might look just that THAT man) is actually not going to assault women, if we can't tell he's actually a woman. That's why I thought it would be useful to tell the difference between the two men. Any ideas?