My grandfather used to say that locks are on doors to keep bad people out. Good people know that they don't enter a house or a car that doesn't belong to them without permission. That's true, but the point that you are missing is this. There have been women attacked in women's toilets by men. Cismen. They were not wearing dresses or skirts: they were dressed as men. Transwomen want to use women's bathrooms to pee, not to check out people there.

I remember, when I was 15, I wanted to go to university to do some research for an assignment and my mother told me that I couldn't go during the day as the gays could seize me and drag me off to the toilet and have their way with me. There are some public toilets that have been meeting places for casual sex for gay men, but they are consensual. What my mother was describing was rather juvenile but most men who rape other men are not homosexual. And most homophobic attacks are conducted by self-loathing homosexuals!

So your argument is erroneous.