Right now I'm going by the public definition, i.e., non white male.
Well that's sort of reductive and reactionary and doesn't really promote discussion.
I think simply put, diversity is showing a variety or representation. Be it gender, color, orientation, ideology, or whatever. Go look up interviews with rappers like DMC or Chuck D where they talk about the effect the Black Panther comic had on them as kids. They LOVED comics before it came along, but once it did, they felt included. They saw a hero that looked like them.
That's just a simple example. A lot of people in various fandoms can love a thing, but when the time comes that they see themselves represented it feels great for your thing to acknowledge you. When geekdom IPs decide to embrace that and be more open to their own fans, that is not a bad thing.
It's a simple fact that most entertainment has always been geared towards the straight, white, christian, male demographic. Not ALL things obviously. IP like Star Trek has always shown diversity (and may actually be the first example of it-- and it WAS a big deal), and obviously niche targeted material has existed for a long time.
But minorities wanting to be represented in the main stream isn't a bad thing.
I get the blowback, because if it is remotely political it has the tendency to be blown up and mutated by the press, and everyone becomes reactionary. But like I said before, you don't get to a place where diversity exists without making a statement first. Star Trek's cast was a big deal at the time-- and even now, people complain that the new show has two female leads.
Marvel's approach in the last couple years was a terrible way to go about it and insulted everybody.
"Pandering" and "gimmick" accusations are so easy to claim because there's no paradigm for these things to happen in a quiet way simply because we're still not diverse as a culture. It would be great if it was as easy as that-- and those of you saying "just cast the best actor" could see that a casting could just be that. Until we are diverse, somebody is always going to cry foul (usually a white dude). We won't be diverse until casting and representation do these things out of rote-- but they don't. They only do it when people make noise.
It's unfortunate, but that's how the message is delivered.
Back to The Doctor, for my money, a female Doctor would be a gimmick and handled poorly if they sexualized her. The Doctor has made it very clear that outside of being in love with Rose and later River, he's put off by the idea of sexuality. To have a female Doctor that dresses slutty and hits on dudes or sleeps around-- that would be a terrible way to go about it.
keep everyone in the dark til the last second. Play up the tension a bit 
