How about stop marketing Diversity as something that makes certain groups special?
I mean it's only controversy bait if some things related to certain characters are ALL that define them and all that they're marketed for.
Do it like, say, The Walking Dead.
No one batted an eye at Lee or Clementine's ethnic backgrounds aside from only one incident I can recall with Kenny in Episode 2 of Season 1, and even that was rather vague. And even still quite a lot of people love these characters.
Some more examples of what I mean is,
[PROTOTYPE2] didn't make a single mention on Heller's skin color.
Just Cause 2 didn't make any special special comments about Rico's race besides trying to make him a campy hispanic hero.
No one talks about Alyx Vance being special because of being a girl or of being of Asian and African descent.
No one made a big deal about how the Prince of Persia was...well....Persian.
No one is up in arms about the main character of Transistor being a girl.
They're all liked (Heller I THINK is liked, I sure as hell liked how hilariously over the top his anger was) not by these tropes specifically, but because they're good characters that quite a lot of people took a liking to.
My point is, don't make diversity a gimmick when making a game, just do whatever you want while trying to hold some significance for the matter of ethnicity if that's the case.
But then there's also fear of backlash.
I mean sure I just consider sometimes that my characters in RPGs like say, Mass Effect, are Muslim like me.
But if there was ever any official Muslim protagonist of a game then it would just lead to everything going up in flames about which version of Islam should said character have been. And knowing how barbaric and animalistic reactions can get, I don't think someone would want to take a chance like that these days until some brave soul decides to try his hand at it.
Because the closest that I've heard about anything close to home POSSIBLY being related to something good is in Metal Gear Rising, the one time they acknowledge Pakistan having a PROBLEM of terrorism not managing to get fully wiped out instead of just throwing it under the bus as ultra-stupid conservative desert country like most media interpretations of the country do (Seriously, as much as I got bored with Iron Man 3 that was fucking cheap with the whole "Rhodey breaks in to a sweatshop full of women working in desert buildings in hijabs thing", the veil isn't a necessity back home and there's only Balochistan that has the most desert in the entire country).
In the end the key is just that the creator roll with it.
Don't make it a BIG DEAL that the character is one thing or another, just DO IT.
Their race, cast, creed, gender and all that stuff can be important if it's important to the GAME ITSELF, not annoying everyone with it by going, "SEE? WE CAN BE DIVERSE, LOOKIE HERE WE ADDED A WOMAN AS A PLAYABLE CHARACTER IN REMEMBER ME, LOOK AT HOW INCLUSIVE WE ARE.". Just an example so no offence to fans of Remember Me, I haven't played it myself but saw quite a lot of the gameplay and story. I thought Nilin wasn't THAT bad, just that her model being a girl meant that the camera kept trying to get in her pants at the worst moments.