You definitely don't have to go out to lunch with somebody to do group work with them. I was in tons of such classes when I was in college, and I can count the number of times I went out to lunch with any of my classmates on one hand...and those were the ones I obviously enjoyed being around enough to actually go to lunch with! (Not to sound like a jerk, but my point is that it wasn't everyone. You definitely don't have to like everyone, just like how not everyone has to like you, either. That's life.)
I think I would try to make it clear without making it personal, so that it doesn't cause unnecessary hurt. So instead of saying something like "Your mannerisms make me uncomfortable (about whatever he is doing that is making you think he is gay), so I don't want to go out to lunch with you", you could say "I find it hard to focus on the project if it is outside of a school setting/too socially focused instead of being work focused, so I'm not comfortable meeting outside of class." Because that is true, right? If I am reading you correctly, it feels like he is being too friendly in a not-professional way with you, and you don't like that, and it is distracting and distressing you. And let's not lose sight of the fact that you were put together in this group to do work and produce whatever the project is meant to be,
not to do lunch and bond and all of this stuff. That would be true even if instead of this guy it was a beautiful lady or something, even if you would react to it differently then. You still have to do the work, and that's the primary thing you will be graded on (I'm assuming), so that should matter most before anything else. It's not like you or your group will get an A+ (or whatever the Polish equivalent is) because you all became friends and found a nice spot to eat and talk together outside of class.
(I swear I'm not antisocial, you guys...I'm just very "type A" about work, because I care about doing a good job!
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