I can actually see where the controversy comes in. I was discussing this with a Doctor Who fan earlier. I'll preface by saying, I'm excited for a female doctor, but a little worried given that the show's writing has not been as strong in recent times.

The worry mainly comes in with the fact that with characters like Iron Man and Thor in the past that we made into women in the comics, there has arisen a trend of taking strong characters and making them into semi-ditzy women. There seems to be this idea among writers that taking a strong male character and simply making them female makes them a strong female character, which is not the case. I believe people are worried the next doctor will follow the same trend. They think that because the show has not had the best writing in recent years, that instead of having a strong female lead, the next doctor will just be a ditzy woman that has no depth whatsoever. Whether or not that is warranted, only time will tell, but that's why I think there's a bit of controversy.