I don't even understand
a. Why he was arrested. (OK, that one is more rhetorical. I guess what I really mean is "What kind of cops have nothing better to do that guard bathrooms?")
b. Why he pled guilty rather than making up some kind of weird but not impossible excuse. ("Those shoes looked like my campaign manager's, so I was messing with his head. I admit it wasn't a very politically correct or mature joke to play, and obviously I'm really sorry, but it was really spur of the moment silliness rather than an actual proposition."* is the first excuse to come to mind after two minutes of thought. I'm sure a political spinmeister could come up with something better.)
*My experience is that homophobic humor is uncommon but not unheard of among congressional staff members working for Conservative congressmen. I can totally see some legislative assistant for some midwestern R doing this to his friend.