"So I'm just supposed to let a person who looks like a man in a dress go into the women's bathroom??"

Yes literally yes. It blows my mind that people still do not understand this. There are zero instances of a person doing this with criminal malicious intent. Public bathrooms are for the public. That means even sharing it with people whose exact shape, size, and color of their genitals could be a mystery to you. You are not the crotch police.

Don't like that? Then fucking pee at home.