Um...first off, if a trans woman walked into a men's room, she's putting herself at just as much risk of getting arrested, plus a risk of getting attacked.
Second-has anybody pointed out to the bigots that they're essentially demanding big, hairy, transMEN use the ladies' room?

Third-I'm androgyne-am I supposed to just squat behind a dumpster in the back?
Actually, I think these people want us all to just go away and pretend we don't exist.

What I say to that is unrepeatable in polite conversation.
My taxes help pay for those public restrooms, so if I'm there and I need to go, to heck with them.