Lets pretend that we cant always tell, just for a moment. How is one to differentiate, how do you differentiate, between an autogynephile crossdressing pervy bloke and a 'transwoman'? Whats the difference? How do we measure it?
Well that's dandy isn't it. You want to condemn people on the basis of the hypothetical. Let's ignore knowing that trans people go through a formal state process of recognition, and that the evidence is that they cause no harm; instead let's ''pretend'' that they do. That's where your argument is at.
Let's pretend that apartheid is always a good thing based on how people look. Let's pretend that genocide is always a legitimate option. Let's pretend it's the 1940s and the Germans successfully invaded Britain.
The state can never guarantee against all risks, and it never does. We don't measure anybody going into public spaces. We live with minimal risk against stranger danger each and every time we leave our house. Statistically for women, they encounter less harm going out than staying indoors with a man present.
Let's consider reality instead. In a public toilet setting, the space outside the cubicles is a public space. Behind the closed and locked door is a private space. There is no loss of dignity washing your hands next to a person of the opposite sex.
How about we just let all people use the public space. That way a man can accompany his wife, partner, girlfriend, daughter, and just wash his hands while she uses the loo. The presence of men will help deter wrongdoing. As a woman, I'm more than fine with that.
I've seen wrongdoing in public toilets. Once in London I was mugged at knifepoint, by three young women. I gave them my purse, they assaulted me anyway for the hell of it. Apparently ''dykes are dirty''. Who knew?
Once in a gay pub in Portsmouth while in the cubicle I heard a violent attack in progress. I came out of the cubicle as quick as I could. A lesbian, known to me as being violent, was pounding her then girlfriend with her pinned against the door. There was blood everywhere, and no way out for me, since like all these spaces there is only one available exit. Apparently she'd looked at another woman.
On another occasion in a pub in Emsworth, I was out with my now partner and two male friends. I went to go to the loo on my own. There was a shared lobby that led to ''gendered'' doors. I went in, came out and there was a man calling himself Alan outside the door wanting to give me his phone number on a piece of paper. I declined, so he set about me. I gave him a bit of a kicking in return and he let me go. I returned to our table visibly shaking. One of the men we were with, then went to the loo, and then to the bar. So we asked ''did you find him?'' ''Yes he replied''. ''So what happened''. ''Nothing we didn't speak, but I've just dropped a lump of my poo in his beer, he'll find it soon enough''. When he found it and yelled his disgust, our friend stood up, stared at him with his arms folded across his chest and said nothing. The landlady was then informed, and the police called.
What public spaces need is a second exit with an alarmed door just like a fire door. Opening the door raises the alarm and provides a means of escape.