So far I've largely tried to avoid this issue. I'm a crossdresser, and while I try to pass, I know I still have plenty of 'tells' that would give me away to anyone who seriously looks at me and tries to guess if their impression is correct or not.
Even at the gay club that I usually go out to when en-femme, where I know both males and females use both bathrooms almost interchangably, I tend to avoid going into either one unless I really need the facility badly. They have plenty of mirrors in the club if I need to check or fix my lipstick, and if I need to do more than that in terms of makeup, I can just as easily go home and come back later, since I live not very far from that club.
When I have used the ladies room, I go in, use a stall, sit, and leave soon after I finish my business, after briefly washing my hands. I don't generally make eye contact or stare at or talk to anyone else.
I suppose if I was in a public restroom in a vanilla establishment and a GG asked me if I was a male, I would reply, "Not at the moment," and then try to leave. If she pursued the point I would say, "If you had not stopped me with that question, I would have already left without bothering anyone, so what, precisely, is your problem? If you had asked that question and been wrong, and the lady you asked had been born a girl, what would you have done? And would you still be upset by her behaving exactly as I did while in here? I have done nothing wrong, and would have caused far more of a commotion if I went into the other bathroom looking like this."
