Fiona Pond
Personally, I have no problem with the idea of a female doctor. I can _maybe_ see where people might take issue--but meh.
As for race. I find it thoroughly preposterous that someone who can suddenly become a different height, different build, different apparant age, different personality quirks, so thoroughly different would somehow be limited in possible melanin level.
I'm willing to argue about whether women and men are fundamentally different. I am not prepared to entertain that the genetics of race are sufficiently relevant to preclude Doctorhood.
I'm not saying that in the Whovian universe, there is anything standing in the way of the Doctor being female, Middle Eastern, African, or Silurian. I am simply saying that in our universe, portraying a character who has for eleven generations been portrayed as a British man, to suddenly change the sex, skin tone, or even accent would be more bothersome than it's worth. In particular, Time Lords appear to have some power over how they regenerate, so unless the Doctor, at the moment of 'death', has some prepossession to become a girl or a Mexican, he overall seems to lean toward the Englishman's appearance, and there's no reason why that should change.