There's a lot of discussion going on about whether the Doctor should be a man or a woman. Once upon a time I might have had an attack of the vapours about casting a woman as the Doctor. When I was young.
Now, oddly I'd be more worried if they cast an American.
But here's the thing. Or one of the things. There is no real reason why the Doctor can't be a woman. Doctor Who is a very long running series with a very inconsistent canon. Hartnell's Doctor had one heart. Now he's got two. For example. Once Time Lords were "immortal, baring accidents", then they could only regenerate 12 times and now...well who knows. RTD put a throwaway line in the Sarah Jane Adventures that implies the 12 limit is no more. Perhaps the Time Lords chucked it out during the Time War. Perhaps it was never more than a societal limit (as there is almost an implication that the more regenerations down the line you are the more mad you might turn out to be). Perhaps after 12 you swap sex?
Basically we don't know. We don't know because 'The Sex Lives of Gallifreyans' hasn't really been much of a topic for discourse.
Now the Doctor has called himself he. He's been a father. And a grandfather. All these words have implications based on our view of how societies are meant to work. But on Gallifrey these constructs could have totally different meanings. There might be a Gallifreyan word for parent that has no gender connotation at all but which the TARDIS translates into father & grandfather to Earth hearing. Perhaps, like in the great Iain M Banks' Player of Games*, the pronoun you hear/see reflects the dominate gender in the culture you live in.
We don't know.
We don't know if the Doctor has reproductive organs or what they look like because it's never - forgive me - come up.
In the Virgin New Adventures Gallifrey is a barren world and has been for a long, long time. 'Children' are woven from genetic looms. Does gender even exist on Gallifrey?
We don't know.
Yes, waking up with a loved one who has changed sex over night would be a bit of shock. If that's the way you society works. But what if that's an accepted part of Time Lord relationships. After all when you regenerate your entire personality gets shaken up anyway. What happens if the new regeneration doesn't feel a sexual attraction towards you? Perhaps there's no stable Time Lord relationships for that reason.
Do Time Lords even have sex?
We don't know.
Perhaps the Doctor's stuck with appearing to be male because he spends a lot of time on Earth and generally - to steal a riff from Louis CK - being white and male improves your chances of being taken seriously throughout most of Earth's history (well, the written Western bits of it anyway) and it certainly does in Britain, where he spends a lot of his time. Perhaps it's a convenience thing.
Or perhaps because most of the Doctor's regenerations are involuntary and stressful he doesn't have a chance to give it any proper thought so he sticks to the male form by default.
Basically the Moffat has revealed that when the Doctor dies he doesn't leave a corpse but a scar in time that appears to be his time line. It's energy. In the old series dying Time Lords have their minds added to the Matrix. Whose to say Time Lords are even creatures of genuine flesh & blood? Perhaps the thing that is a Time Lord is a creature of pure energy that choses to hang about in a flesh suit for old times sake. Or not.
To cut a long blog short. There are reasons why the Doctor is a man. There are reasons why we're comfortable with that. But there are also a reasons why it doesn't have to stay that way and I might not even have thought of a tenth thousandth of them.
Personally I don't care. All I want is a good actor.
And if we get another man and we want the a woman Time Lord perhaps we can get the BBC to make Romana: The Series or Jenny: The Doctor's Daughter.
Doctor Who is an sf series capable of adapting to big changes. The Doctor being a woman might be a shock and it would be a brave actress that would take on the part knowing that if it all went horribly wrong her casting would be the reason given.
Sorry...back to the conclusion. Fundamentally if the Doctor changes sex the series can find explanations for doing so and if he doesn't, he doesn't. The Doctor Who rules are extremely elastic. There is no bible or canon that people can agree on.
And let's face it Doctor Who fans can find reasons to dislike a current Doctor without gender being an issue.
*RIP Iain M Banks btw. Writer of great books. Much, much too young.