I think a legitimate criticism of casting a woman in the role is that whilst fiction is all made up anyway, it ¡'should'! follow it's internal continuity rules within the universe that's been created, and in 50 years there's never been anything built into the continuity to allow a time lord to change sex on regeneration, Missy notwithstanding - if they were going to do it, then they've had nearly 15 years of the new series to do a proper job of laying down some backstory conditions to enable it.
The counter-argument to that is all the way through its history the show has played fast and loose with its established continuity, whether that's been out of convenience to solve a rabbit hole they've gone down or whether it's because the producer and script editor at the time have simply forgotten something. The various alternative histories of the Daleks, the date settings of the John Pertwee U.N.I.T. stories (and indeed the modern reverse engineering of UNIT to be Unified Intelligence Taskforce rather than United Nations Intelligence Taskforce), and Robert Holmes just making up on the fly the 12 regeneration rule are the biggest examples.
And arguably the show has been at its weakest when it's been hidebound to its continuity knots, and stronger after the occasional reboot!
I do though think it's a shame the role has become so politicised that whatever the sex or race of the new person to be cast as the Doctor, there would have been one group or other who would have been outraged at the decision.