Just a quick, back of the envelope, tally of the responses here shows a real tendency to focus on, let's call them "familiar" subjects. Vast majority of people are talking about left-right politics for instance. Or sex, race, sexual orientation type things. Or inequality. (ie-Housing affordability.) But none of these really contribute in any real way to the lack of diversity of ideas present when brainstorming, say, new uses for nanotech.
We do have a monoculture of beliefs. Everyone believes, for instance, that diversity only means political diversity. Or gender diversity. Or religious diversity. Etc. And so, that becomes the center of our focus. But political diversity, for example, is not even terribly valuable when brainstorming solutions. Gather some Stanford/Berkeley grads along with some impoverished, but clever Africans and Asians, and I'd bet you'd be able to hit on more innovative solutions to more problems than you ever would with a room full of political liberals and conservatives parroting their respective dogma.
Diversity of thought like that is difficult to achieve because, ironically, of our belief that diversity of thought means diversity of political thought. Or diversity of race. Or diversity of gender. Etc. (All of which are next to useless. Especially since all of that diversity is coming from the same overall culture and socioeconomic class in most cases.)
If you want the benefits that diversity of thought conveys, you can't look for comfortable substitutes for it, like religion, race, politics, sexual orientation, or gender. Going to find a religiously diverse team, which inevitably thinks like you, or a politically diverse team, which is even worse in terms of sameness, won't work. You have to go all the way. Not only should their thoughts be diverse, the fundamental way they think should be diverse if that makes sense? (I once gave a presentation at Halliburton, and I can tell you, having someone around who thought about logistics in terms of donkeys was extremely helpful in terms of solution finding and problem solving.) If you're not willing to go all the way with diversity of thought, you're not going to get the benefits of diversity of thought.
You can hire more women, or conservatives, or muslims, or hispanics, but it won't really get you anywhere. You need people who think fundamentally differently than other team members. And you might even need people who think fundamentally differently to even identify people who think fundamentally differently. You don't FILL the team with those people, (you have to be able to get work done), but you should make sure a few of them are at the table if you want to reap those benefits.