Late to the debate also but been following with interest. The thing that confuses me is that gender identity seems to vary from era to ear and culture to culture, so the idea that they are 'innate' or 'fixed' seems a bit strange.
For example, at the turn of the last century, it was extremely shocking for a woman to wear slacks. If you don't believe me, 'women and trousers' has it's own wikipedia entry. Women could and often were fined for wearing trousers. Then along came WW2, and women whose clothing was rationed, and whose husbands were away started wearing their husbands clothes for the war effort (that was another huge change, women working outside the home, when the argument that women staying at home was 'natural') - trousers were practical and it meant that women could save their clothing coupons for things they actually wanted. At the time there were raised eyebrows that women wearing trousers was 'not natural' and that women would become 'too masculine'.
Today we would not and do not bat an eyelid when a woman wears a pair of trousers. And we are not confused by it either. Everyone knows it's a woman in slacks - whether she be wearing jeans, a power suit, an army uniform. We are not confused if she's young, middle aged, lesbian, even butch, she's still a woman wearing trousers. Contrast that with our current response if a little boy wants to wear a dress.
Back in the 80s when I was a teenager, I vividly remember the hoo ha when Boy George rose to fame. Here was a gay biological male wearing dresses and playing around with gender stereotypes with his hair and make up. I can remember the press specualtion, was he gay? Was he androgenous? Was he a woman? It seems to me we have no confusion that he's a gay man playing around with gender roles. Same with Eddie Izzard now, he's a man, he's straight, he's in high heels, make up, has a beard, wears a pinstripe suit and nail varnish. It's not even shocking really.
I think the problem with this debate is it conflates sex and gender. Sex cannot be changed, gender is a moveable feast. Gender is also not binary, it's hierarchial - in our culture masc characteristics are definitely viewed as more valuable as fem characteristics, which is why most jobs that require feminine characteristics (caring, nurturing, listening) are so badly paid vs jobs that require masc characteristics (aggression, cool rationality, ruthlessness e.g. merchant banking).
I have a very old copy of a Wive's Manual called the Total Woman - it's not a spoof, it's a handbook, written in the 50's that tells women how to be a good wife. There are things in it like, always rise before your husband wakes and apply make up, he must never see your bare face. Or wait until he's gone to work before you use the toilet to empty your bowels. Or when he comes home from work make sure to never complain about your day. Stuff that even the most adamantly 'not a feminist' girly girl today would laugh at.
Again if 'gender' is innate, how come it changes so much. Are we saying that if a man wanted to be trans in Saudi Arabia, all he'd have to do is don a Burqua and stop driving and that's it, job done?