"I’m pretty sure that I would have found my feminine side and said, ‘Coach, I think I’d rather shower with the girls today'"
Said the chubby man who would be President. That's not a pretty picture and not a picture I enjoy holding in my mind, but the point is that the rabble rousing that involves scenarios of some guy dressed as a woman raping your daughter in the Lady's Room is fiction. If some dude wanted to dress up and explore the fabulous world of toilets, there would be no law likely to stop him, no DNA test or passport control at the door. Indecent exposure laws, where they apply, are still in place.
Transgendered people have been using washrooms of choice for decades and so far, I don't know of a problem, nor (and I've asked) do women normally walk around naked in public toilets. Sorry, Mike, the athlete formerly known as Bruce Jenner isn't going to molest your wife or your darling daughter nor will anything be exposed outside of a toilet stall. You'll never know.
Frankly, remembering the alarming record of Republican politicians who rant about sex and gender and protecting the world from homosexuality being caught doing naughty things to boys in cloakrooms or sitting with "wide stances" in airport mens' rooms and sleazy motels, I'd rather not share a bathroom with Mike at all. Methinks the fat man doth protest too much.