I find the 'what if you woke up in a man's body tomorrow?' argument as evidence for innate gender very strange. Yes, I'd be very alarmed and uncomfortable if I suddenly woke up as a man. I'd be equally uncomfortable if I woke up as a woman with a completely different body to my own. Because body switching is inherently disturbing.
Also, if I woke up as a man, I'd have a male body, and regardless of how I felt about that body, I wouldn't take myself off to the women's changing rooms, because I wouldn't want to make other women uncomfortable. Basic decency.