Yes. Because he is a man - and therefore belongs in the men's room. Women should have the right to use the restroom facilities without concern, fear, shame or embarrassment they may feel with having a man in the room with them. It is of course not only children one has to worry about . But, no woman for her own safety should EVER be in an enclosed space with a strange man she does not know where they could possibly overpower and assault them.
Practically speaking - if he is pulling off his drag that well, its likely no one will know, so no harm no foul if he does use the women's room.
The differnece is though - the legal right of business owners, or the police to question a person, or prohibit a person who is a man from using the women's room. If I know for instance that a regular customer is a man dressed as a woman - and my other customers know and don't feel comfortable having him use the restroom facilities - then it should be my right to tell him he must use the men's facilities. If someone is not in full on drag but more like a "pat" from saturday night live, and is also making my other customers uncomfortable, then as a business owner, I should ave the right to ask - and direct that person to the men's room. Or my other customers should ahve the right to tell him he is making them uncomfortable.
Besides which this even a bigger issue in locker room facilities. They are single gender for the comfort of the people using them. So that women - who are modest - have the ability to change in a facilitiy where they can not be observed by men. For many, this is even a critical part of their religion and they would suffer great shame at having their body viewed by a man. It doesn't matter what HE thinks he is - it matters what other people know that he is.
connie