I could be wrong of course but I think it's a vocal minority pushing for diversity and that most gamers couldn't really care less what colour/race/sex a character is.
How many people are going to not play Call of Duty if it has a black leading character? None. How many will not play Overwatch heroes because of their skin colour or sex? I'll go with none...
I'm really growing tired of articles about how 'X is So White' (Polygon just did this about Star Wars). Websites that get so bent out of shape about skin colour seem more racist to me than anyone else, when I see a movie poster I don't count the number of whites vs. others...
This right here is why it's such a big issue. I'll note now that I don't mean this as an attack on you @wynnduffy since I don't actually know anything about you so I can't assign any personal attributes/thoughts/feelings to you, just quoting because I think the ideas in your post are pretty illustrative. Now onto the point.
The idea that nobody cares about race/sex seems very indicative of privilege. White males not understanding why people get so bent out of shape (again not assuming that @wynnduffy is a white male) about skin colour of characters is precisely because they don't and never have felt under-represented in media and don't need any extra empowerment. So in some ways, it's totally true that it's a vocal minority, because that's what we're talking about with this idea of diversity in games is representing the under-represented minorities.
If you're right that people aren't going to not play CoD if it has a black leading character, then all the more reason game devs should make efforts to have black leading characters so that the people who don't care can go about their business but the people who would be happy to play a character they more easily identify with or feel represented by would get, well, representation!
Same goes for gender diversity, since that's what the thread is originally on. This is especially so since women aren't actually a minority in the real world, so it doesn't make sense why they should be so underrepresented in games.