you’ll accept an alien with two hearts but not a woman? 

Yes, because we have always had the Doctor be a BOY and his companions be kick butt GIRLs. That is how it works and should stay. A female will not be right for the Doctor.

I actually don't really care if the doctor male, female, black, white or even a green bug alien, as long they found the right actor (or actress)
it's hard to be the doctor, you must have something special, not all people can do it, no matter how great an actor they are