It's clear that he doesn't want to offend the minority though because he makes things so ambiguous with what even side girls are doing with other guys. It's clear that Rio, Sarah, Mel, Cam and most likely Quinn are doing stuff with other guys while the game is happening, but DPC gives plausible deniability to it so that fans of those girls don't get offended. You see that with some (not all) of the Quinn stans in this thread who claim that Fuckface was the only guy she's presented herself as a menu option for in more than 2 years of the restaurant, and that she had enough power over Burke and Rio at the start of the restaurant that she could force Rio to fuck Burke but didn't have to do anything herself if Burke told her to.
If we join Quinn and Sage at the cafeteria in episode 6, this is the conversation that we witness:
mc "How are you today?"
mc "I know. It's an obvious answer to that question. I just wanted to break the ice."
qu "We're not talking about that now. Ok?"
mc "So, what are we talking about?"
qu "Sorority things."
mc "I don't have much to add to that. And I'm guessing we're not discussing DIKs and HOTs either."
mc "So...uh...what about that HOT scavenger hunt? It ends this week, right?"
qu "On Friday."
sa "Speaking of that, you'll have to take care of the preparations."
qu "Yeah... I got it."
qu "If you want, I can take care of the entire thing."
qu "You should take some time off."
sa "You know what to do?"
qu
"I have your notes and I remember how we were treated last year."
That seems to indicate that Quinn joined the sorority the year before.