I read an article once about the hijra, a third gender in India. What surprised me at the time was that some hijra were adamant that they were not transgender in the western sense, seeing it as foreign and strange, whereas others would have preferred a binary transgender identity had it been available in their culture. So some strongly viewed hijra as what they really wanted to be, but others saw it only as a consolation prize because their culture didn't include the concept of transitioning to the other binary gender.

I walked away from this thinking that the cultural component of gender can't be overlooked. Gender is ultimately a compromise between the individual and categories provided by the culture. I can even imagine, that if one had two very different cultures and were able to completely replicate a particular infant, atom for atom, it's possible in one culture they would identify as male, and in the other as female.