The idea that the 'social warrior' is never out to exclude others is ludicrous.
Now, I acknowledge that this isn't the case for the majority of people who cry out for inclusivity: most just want as many demographics represented as possible, and I respect that. Also, this opinion is built mostly from news sits, as well as interactions on blogs and on youtube (i don't get out much) so take it as you will. But there's increasingly an idea in our culture that being fair to a culture means excluding whatever is currently considered the dominant force.
It's a bit of an extension of the black/white, right/left culture you bring up here. If you want to be on the side of gay rights, you absolutely must oppose even mentioning the bible. If you're against the Democratic party, you must be /for/ the Republican party(**). If you're pro-life, you must want all women to be, and I quote, 'chained in the kitchen to serve as your personal incubator'.(*) Hell, I only call myself conservative because other people kept /telling me/ I was when I brought up my opinions on social and economic issues (say, 'we should let the markets do as they please' or 'yes, I trust businesses more than I trust Washington D.C.').
However, there seems to be a growing group who think that the best way to be inclusive is to do everything in your power to expunge anything that might offend anyone. The idea seems to be that some things are so offensive, so abhorrent that we shouldn't even acknowledge they exist. It feels less like putting Elizabeth and Booker together on the front of Bioshock Infinite, and more like relegating Elizabeth to the back: hiding something that's very much present in an attempt to make others feel better. Essentially the exact reverse of what 'be inclusive' is supposed to mean.
Unfortunately, this attitude breeds hostility on both sides of any given issue, probably even more than simply putting the offending thing in would have. The reason that many people treat inclusivity as a zero-sum game is because so often being inclusive is framed not as a question of allowing someone else to stand in the spotlight with you, but a question of who to shove out of that spotlight. This nativity scene in someone's yard needs to go because it's offending some atheists from a city over whose lives this couldn't possibly affect. This man is wearing muslim garb, he needs to be thrown out even though he's not doing anything! This woman's opinions on the market might annoy me, let's publicly shame her and get her pulled out of that conference! This person doesn't like Anita's videos, therefore they're exactly the same as the people who threatened to rape her, etc etc. To let something else shine, you have to knock something else back into the dirt. It's absurd, I'll grant, but this is unfortunately what so many self-proclaimed social warriors keep on doing.
Again, I must stress, this is not the case for most people who want things to be more inclusive and (as far as I can tell) is definitely not the case for this particular incident. It's an option in a game, it only affects you if you want it to. The attitude's just present enough and loud enough to breed a toxic and hostile enviornment whenever social issues that should be a no-brainer crop up. (also a lot of people on any side of a social issue are idiots, but we knew that already)
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(*) The especially ludicrous thing was that (iirc) I'd already said I was asexual and celibate >.>
(**) The Democrats have all the sincerity of the Ebon Dragon (for people not familiar with Exalted, basically none) and the Republicans couldn't sell a loaf of bread to a starving man. And they're both more corrupt than a guy named Corruptus McEvilguy who sells poisoned snow to eskimos saying it's candy for their children.