"The Doctor has been a man for so long because the show’s narrative choices have been constrained by the misogynistic expectations of society. [...] a female Doctor would have been a hard sell." -- Galen Mitchell
Or, maybe Ms. Mitchell, the show's writers or creators found an actress they felt was the right fit and changed the dynamic of the show. Dr. Who is not some 1950s medical show. I suspect the show's creators aren't overly worried about being constrained by the misogynistic expectations of society.
"there hasn’t been one [GLBT rally] demanding an LGBTQ doctor on a fictional television show" -- Teresa Latimer
Maybe not specifically demanding a transgender time-traveling shape-shifter, but there have been campaigns to promote more GLBT characters in fictional TV shows.
My two cents? Jon Caldara was creating controversy. He admits the show's producers use shape-shifting as a device to explain changes in actors. So the producers hired a female actress. No other agenda necessary.