Yeah, I think the whiteness of the Doctor is much more "fixable" than the Doctor being male. As far as I know from the canon I've seen, Time Lords don't seem to have racial identities apart from being Time Lords, but they do have a variety of skin colors, etc. So a Doctor who (by human standards) was black or South Asian or East Asian etc. doesn't have the same canonical obstacles in its way. The change could be genuinely meaningless to the Doctor, but not at all meaningless to the humans he encounters, and that if well written could be extremely interesting.