“He is wrong on this gotcha question which is not surprise. What can he do to change it?”
Nothing. The LBGTs are a federally protected class which pretty much eliminates any states rights arguments. Community his and hers bathrooms are an antiquated concept and have long been a magnet for all sorts of illicit activity.
Public bathrooms will have to be remodeled to single occupancy unisex water closets. It’s the only answer.
That seems like the safest thing to do. Each person enters a single bathroom that has a lock and there is a sink. Perfect privacy and security. There have been attacks and even murders in public bathrooms even without a transgender bathroom law.