I see. How can you tell the difference between a transwoman and a 'cis' man?
There are lots of people who, when you look at them, could be a cis women, a cis man, a trans women, or a trans man. Unless you expect all people to be gender conforming, there are times when it is simply impossible to tell from looking at people what genitals they are born with or which gender they would claim today. Some women are tall, heavy, muscular, have slim hips or virtually no breasts, some have facial hair, sharp jaws and prominent facial features, some have deep voices and masculine mannerisms. Some men are short with higher pitched voices and soft features.
Of course there are people that when you look at them you just know, but it's simply true that there are many people that when you look at them, you just don't know.
I do not believe that people who look different from the gender-based norms should be required to exit facilities that they have a right to be in simply because other people are afraid of them.
We used to be in a situation where black women, or lesbians, were not welcome in women's facilities because people were afraid of them and would cause harm. It wasn't right to exclude them now, and it's not right to exclude people now.
It's not just about how this affects trans people, either. This idea of judging people based on their appearance hurts cis women, too. In fact, it's statistically more likely to hurt cis women. I've even been a victim of it myself. I'm not trans. I'm short with long hair and when I'm wearing makeup, you'd never question that I was a woman. Yet if I'm wearing a hat (e.g. in winter), no makeup and a nerdy t-shirt, I could be either a woman or a boy. I walked into a Tesco toilet once and had a woman yell at me that boys aren't welcome here.
When we enable a situation that it's okay for people to judge people based on what they look like, and that people's eligibility for facilities should depend on whether other people might be afraid of them based on what they look like, this hurts everybody.