The biggest complainers are the ones who get an idea in their heads and decide that X version of a fictional character is the only one possible, and any variation is blasphemy. “Superman can’t be black!” they scream, ignoring the fact that Superman isn’t even human — he could be green and polka dotted (although that might make his secret identity a bit tougher to hide).
Sometimes it really matters whether a character is male or female, black or white … if it’s important to the plot. And sometimes the writer/director/producer decides to go against the expected to make a point or to do something different with the character.
Re-interpretations of fictional works happen all the time. Look at how many times Shakespeare has been done in a new way. Characters can change race and sex; the story can take place in the present or the future — it’s fiction. You can do that.
With Doctor Who, it’s even easier to change, because the Doctor changes. Since the show has been going on for 50 years or so, the same actor has not played the part and so the writers came up with “regeneration” where the Doctor sheds his old body and takes on a new one. I’ve never understood plot-wise why that has to happen, but I certainly understand why that needs to be done for TV’s sake. And there is nothing in the established history of the show to indicate why the Doctor regenerated as male the last dozen times (or, for that matter, why the aliens always seem to be attacking London, but that’s a separate issue). So what’s wrong with a female this time? Statistically speaking, shouldn’t that have happened long ago?
For that matter, what’s wrong with changing real, actual history for dramatic purpose? Hamilton features minority actors playing the white Founding Fathers, and they did that to make a specific point, as well as to say, “Who cares what color the actor is that plays this part?” The story is still plenty strong, the characters are believable and real, and so what if they don’t look exactly like the people they’re portraying?