Is it Dr Who fans who are complaining? Is there a reason the Dr couldn't be a woman? Doesn't the Dr regenerate, so why not into a woman? Was it done for PC reasons? Probably. But after decades of evolving storylines and new doctors, I have no problem with the Dr being played by a woman.
Similarly, I don't have a problem with Watson being played by a woman in Elementary, or if they want to have a black James Bond. That is, as long as they are modern takes on the characters. But don't try going back into the 1800's and make Watson a woman, or back to England in the 50-60's and make Bond a black guy - or a woman.
My guess is that they'll have the new Dr hidden under such frumpy clothing that you'll be hard pressed to even tell that she is a woman.