I admit that I haven't seen the latest season past the second or third ep yet, because of... the lackluster writing. I love Capaldi's Doctor, though, but the stories so far have been not that great, and I don't like Bill at all.
And I have to agree with Spectre. I don't have a problem with casting a woman as Doctor Who. The character is an alien from a fictional species that regenerates upon death into a new body, so what, it's no biggie switching the gender. It has been handled very well with The Master before.
I do have an issue with the move blatantly motivated by political correctness, gender diversity, whatever you may call it. There has been so much talk for such a long time about making The Doctor a woman, or black (why not Asian, though?), or both, that the casting just cannot be sold as "we have a great actress who can play the character in the direction we want him/her to go". It is "she was cast because this time, it had to be a woman". And this kind of following the PC lead also does not inspire confidence in the writing getting any better in the future.