I'm trying to consider all things, here.
Doctor Who has been a BBC staple for generations. That doesn't mean it has always been good.
In fact, the reboot has been very rocky. Aside from a much better look and budget (still, at times VERY cheesy), the reboot has seriously struggled with writing quality. Yes, there have been a few (a FEW) very brilliant episodes. But overall, the show has deteriorated to fan-service and techno-stupidity.
It has been the equivalent of Star Trek (TOS) third season and X-files (most seasons) for most of its run.
I have only caught the first 2 episodes of season 11. Despite all the hoo-ha that the doctor is now a woman, her character for the first two episodes has been quirky, funny, frenetic, charming and endearing. Yes, it's derivative of sorts-- everyone has been looking for the next Tom Baker. David Tenet was the closest, but the show still struggles with finding a balance. They have yet to get relationships straight (no pun intended there). I was always creeped-out by the Doctor/Rose relationship and the doctor needs to exist on a separate plane from his/her companion(s).
The key to a successful Doctor Who is singular and the show-runners and producers keep missing it. It's the writing, stupid. Get top notch sci-fi talent to write deep, meaningful episodes and it will work.
I think I would be okay with a female, black, dwarf, or two-headed doctor IF the show were well-written.
It isn't.
It panders to stupidity, generations of TV viewers who had no choices of what to watch, and fan-service.
Even the blind squirrel finds a nut on occasion (e.g., "Blink" and that episode didn't even NEED the Doctor in it at all).
I'd be more than happy to give her a chance if they could find real writing talent.
Showcase/Canadian Sci-Fi is way smarter overall.