Note: I have never seen an episode of Doctor Who.
But!
If the series premise is that actor changes are really the Doctor undergoing a change in body, then why can't the body be female? And if the body is female, why does that necessarily represent a blatant political statement by the transgender community? Maybe the show creators or writers decided to give a female Dr. Who a try?
People have talked about a female James Bond. Without pushing a transgender agenda. And, no, I don't think Atomic Spy is it, unless we're talking in the Daniel(le?) Craig mold.
I remember a Star Trek: The Next Generation episode, where Dr. Beverly Crusher falls in love with a space alien who is a parasite living in a humanoid host. Every so often, the host body fails and the alien has to find a new host. Dr. Crusher knew this and had told herself she was prepared for it. At the end of the episode, the alien gets a new host body, and rings Dr. Crusher's door. It turns out the host is female. Roll credits.