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I agree that sometimes they make rather unfortunate choices in terms of emphasis. I have nothing against the agenda as such, but it should benefit the plot and not detract from it; there are many good examples of this, but unfortunately, Doctor Who is noticeably lacking in this regard. The BBC is too focused on Disney, which also has Tolerance (TM) and Inclusivity (TM), but if, after buying the Star Wars franchise, they had made a sequel trilogy (I'm speaking hypothetically, because everyone knows that Disney didn't create any content for Star Wars; there are only six films by Lucas) and included a black character in the main cast, he would magically disappear from the Chinese poster because the Chinese don't like black people, but they do like to spend money at the cinema.
And the talk about a female Doctor first appeared in the classic series. Tom Baker, who played the Fourth Doctor, mentioned when he was leaving that a woman could play the role after him, and since then, such rumors have consistently circulated with each regeneration. I saw a clip of an interview where Patrick Troughton (the Second Doctor) was completely in favor of this idea, and he didn't even live to see the full-length film with the Eighth Doctor. Plus, Romana, a Time Lord/Time Lady and companion of the Fourth Doctor, was something of an attempt at a female version of the Doctor, especially after the character's regeneration; this is even more noticeable. So, they didn't just belatedly realize the idea of a female Doctor; they realized it catastrophically late.