But you seem to be intentionally overlooking GP's main point -- people (dare I say most people, probably) have that strange hangup that they really prefer to visit the restroom with people of the same biological gender.
And before somebody comes back with "at some point people did not want to share bathroom with people of a different race", there was a movement to make people see folks of other color as fully human. There is no movement to make people accept seeing naked people with different genitalia.
(added) I don't think anyone is arguing seriously that transsexuals should not use public restrooms, period. But which restroom to use isn't quite as simple as "whatever gender they identify with", unless you believe that others have absolutely no say in the matter.
The fundamental difference that will not allow us to converse well here is that you are intentionally not accepting that a trans person is the gender they have transitioned to.
It's clear that's the case from, for example, you saying "to keep women safe" and very obviously not including trans women in that group. Trans women are women and also deserve to use the bathroom where they will feel safer.