That got me to thinking: While the Doctor is a very "human" character who believes in doing the right thing and loving his alien neighbor, he can also be a despicable bastard as I've previously said. A female Doctor would have to be portrayed the same way - attention will have to be payed to the fact that we are still watching the same Gallifreyan who loves to be clever and impress his/her companions and hungers for the limelight. Not only that, but a character who has killed millions and can be a very cold and devious chess-master. Would feminist groups be upset at seeing a female Doctor portrayed that way and cry foul? Would they claim that the female Doctor is being painted as a narcissistic showoff at the least and a nasty unlikeable bitch at the worst, and that this harms the image of strong female characters?
You seem to spend a lot of time worrying about what feminists
I offer up Maleficent as an example. I just saw the new film and it surprised me at how the titular character is portrayed. The film tries to paint her as a morally ambiguous character with a lot of darkness around her and who is capable of awful evil acts. But at no point does she directly kill anyone in an act of deliberate murder. It's as if we as a society can't quite handle the idea of a female protagonist who is a good person and a cold blooded killer when it's often celebrated about many male protagonists, or if it's a ridiculous action schlock movie that should under no circumstances be taken seriously (see Resident Evil). In a perfect would, a hero who is also a killer should never be celebrated. The character of the Doctor certainly isn't intended to be celebrated for the sentient beings he has killed. But since he is a male, most fans don't demonize him. The show even goes out of its way to scold the Doctor on one occasion - Agatha Christie calls the Doctor out for being excited to solve a murder mystery as if it were a game, when real human beings were being killed. Would fans demonize a woman for doing the same things? Or would they see such a character as empowering for women? Because that would absolutely be the wrong message.
Why would the fans act any different because the character is a woman? You're whole argument is based around what you think other people will think.
Even there your logic confounds me, you claim:
(1) Society can't handle a female protagonist who is a good person and a cold blooded killer.
(2) Male protagonists are often celebrated as a good person and a cold blooded killer.
(3) In a perfect world, a hero who is a killer would not be celebrated
(4) The Doctor isn't intended to be celebrated as a killer
(5) Most fans don't demonize him because he is male
So going by these statements wouldn't a female Doctor be more likely to be demonized for being a cold blooded killer(1) and if she were demonized then that would be a good thing(3)(4), no?
If a female Doctor wasn't demonized than it would be no worse since males are often celebrated for being a cold blooded killer(2) and fans don't demonize the Doctor because he is male(5). In fact, if she wasn't demonized statements (1) and (5) are even more shaky.