Oh, no. Nice try, but you can't have it both ways. If women want gender equality, they're going to have to give up any special treatment they might've received back when the mentality was that women were meant to be cared for and protected. That time's over and done with. It's dog eat dog and bitch eat bitch now. I don't give ladies my seat on the bus, nor do I stand when one comes to the dinner table. I certainly would not consider opening the door for one, simply because of their gender.
As for Diplomats receiving reserved parking, I'm fairly certain that falls under handicapped spots for the mentally ill.