What the conservatives seem to envision is a scenario where a sociopathic individual uses the rules that would allow them to masquerade and gain entrance to a restroom where they might perpetrate some violent criminal acts. Rapists are already a problem so it seems like a far fetched concern that they would dress up in drag first. Voyeurs could take advantage of the rules to set up digital devices to record the goings on. It's about the only thing I can imagine.
I don't think this issue is important enough for the federal government or any government to make laws about it. For Christ's sake, if you got dangly bits, you use the boys room. If you look enough like the sex you identify with, break the fucking rules and use the restroom you wanna use. Fuck it! If you think you look like a _________, then be a ________ and use the restroom you like.
Fun fact: My nephew, in his early twenties, refuses to use restrooms anywhere and he will drive home to take a dump if he has a sudden urge. He'll be out to dinner with family and will excuse himself for a road trip. LOL craziest thing I've ever seen. I've never asked him what the problem is. Apparently he has a delicate constitution.