My two cents:
I sometimes use an STP, most of the time I dont because i'm still getting used to adjusting and using it quickly without fiddling too much. I always use the mens rooms and havent been questioned. Guys won't question you because they don't pay attention to others. They go in, go toilet, and leave. Men also don't talk in there, so if I guy asked if you were supposed to be in the mens room, he would draw attention to himself. I sit down to pee and no one has noticed. I was really nervous at first too, but had an ftm friend of mine just pull me into the men's room, and I realised it wasnt as scary as i thought it'd be.