I've had this conversation several times on RF, and I cannot recall whether you and I have had it or not, so here goes:Since we don't check the genitals of people entering rest rooms and it doesn't sound like you want to be checking the genitals of people entering rest rooms, then your question about what genitals the person has is rendered moot, wouldn't you say?
The thorny problem is that some trans women do not care if they look like men. Some of them even have beards. So this means that PEOPLE WHO LOOK LIKE MEN are going into women's safe spaces. restroom, locker rooms, safe houses, shelters, and so on.
I don't think that having genital checkers is a good solution - hey, we agree on that point!
But further, in a locker room situation, even if a trans woman looks like a woman, if he still has his male genitalia and if he undresses in front of other women, he is disrespecting their privacy rights, possibly even their religious sensibilities.
This is a real, thorny problem.