I am not against a woman Doctor or a black doctor, but they need to remember things like racism and gender bias through the ages when they visit those time periods. A woman or a person of colour would have been flogged for speaking, let alone trying to tell white males what to do.
One thing Doctor who used to do was teach the kids a bit of history here and there, you cant turn your back on reality and pretend that these things never happened.
Have a Woman, a black man, or even a black woman, but don’t insult them by not acknowledging the persecutions and hardships that they have faced when in those times.
It doesn’t have to be the focus of the episode, far from it, but it can’t just be ignored as well.