To this day when I tell people I went to UT Austin their first response is usually "Longhorns are doing great this year aren't they?"
"I have no idea" I respond. "But they have very good EE and CS departments."
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.
Some people are full of shit, but hide it until they are more successful, which often correlates with age, and then stop to care and show the world their real face.
I also think we might have different ideas of what "not giving a fuck" means. To me it's about being true and at ease with myself, even when I'm uncool or weird. It certainly doesn't mean being an asshole, rude etc.