>Conservatives of the flavor you are talking about consider trans-women to be men.
This point is not lost on me. I noted it in several of the posts that you're replying to.
>They don't need to differentiate
To enforce the rule, they need to differentiate between transwomen and cis women, since they do not consider the former to be women, and think that cis women, but not transwomen, should be allowed to use the women's restroom. You acknowledge this yourself in other parts of your post.
>In practice, if they wanted to enforce their rule, they could just require ID to use a toilet and require that the ID specify gender at birth (as verified by birth certificate). The current state of the person's genitals does not have to play into it.
This is a weird and pedantic objection. You're saying that they care about whether or not the person in question was born with a penis rather than whether or not they currently have one. Ok, but so what? Then you have to ask everyone who goes to the women's bathroom whether they were born with a penis.