I'm torn about the new Doctor...
...not necessarily because she's a woman now, but mainly because of the recent male-bashing SJW crap writing the show has had in the last few seasons, even when Capaldi was the Doctor.
I think there's nothing to say that a Time Lord cannot change gender, if they can change their appearance so radically and even choose what form their regeneration should take (ie. Romana) and so I think it's not unreasonable to assume that they can change gender, too. After all, Missy happened, and so that's that. As far as I understand it, Time Lords have even regenerated into monsters that had to be destroyed, so anything's possible.
But Doctor Who for me has been spoiled in recent years with too much emphasis on Clara and identity politics and SJW crap, and so my enthusiasm for the show has cooled in any case. However, I like Jodie Whittaker and would like to see her do well, as long as Chibnall doesn't give in to the SJW crapfest. Last night's episode was a good sign.