When somebody tries to talk sports to me, I feign stupidity but in a silly way. For example if somebody tries to talk Football (American) I say "Oh, that's that thing where sweaty guys chase each other around and people talk about it, right?" and they laugh, realize I have zero interest, and we move on to a more relevant subject. It's all in how you go about it.
Sports fan: "Did you see the blank game?" Me: No but isn't what's his name doing well?
99% of the time people will fill in whoever the star player is and talk about how good they are doing or say no they were doing well but they haven't been recent.
I didn't care much about sports when I moved to Chicago, which cares a lot about sports, but now I have some knowledge about all the teams and friendships with a lot of sports fans I wouldn't otherwise know well. Go Bulls.