I agree that gay Bond would be a bit daft, given how ingrained the character's sexuality is to the role. Similarly a wheelchair bound Captain America wouldn't work - that also doesn't go with the fundamental essence of the character. But what's wrong with the idea of a black Spiderman? Nothing fundamentally white about that character, it just happens to be the way the comics were originally drawn. If rebooting the franchise is OK at all, why couldn't it be a black science geek who gets a dose of radioactive spider venom this time around?
None of these gender or race issues applies in the case of Doctor Who. Due to the regeneration meme the Doctor could quite literally be played by anyone the show's creators want to hire for the role. The show runner just has to play it straight, not treat it as some kind of big novelty themselves.
The new Doctor is female - so what? Best of luck to her - I'm looking forward to seeing what she'll do with the role. If she's anything like as good as Michelle Gomez was as Missy then we're in for a treat.