This is not an answer to the question posed, but I will address your point. We as a society do have protections against predators accessing single sex spaces. A sign identifies a single sex space, our eyes monitor it, membership are another level of protection, basic knowledge our shared values within social contract, that common decency a poster mentioned, and our laws all uphold how society operates its single sex spaces.
If you alter the control measures of our single sex spaces how do you not increase risks to females rights to decency, privacy and safety?
One of now numerous questions you have avoided .. If we look at safety. To state allowing trans people to use women’s facilities wouldn’t therefore increase risk (threat), you would have to be able identify that trans people display sexual patterns that parallel females. Can you identify that evidence? You above have highlighted how one male entering womens facilities increases a risk. Why doesnt one trans individual do similar?