In the U.S. we often say " I don't do___" to signifiy that "It's not my thing", or "I'm not that into that", "I'm not a big fan", or that is "I don't particularly like that thing".
--> Are you big on sports?
--> I dont do sports.
In any other case if you dont want to emphasize that you dont like sports or aren't so interested in it, you would just say "I dont play sports/ football."
They might ask you "do you like___" but here "Do you" means "are you in the condition of". But "do" probably wont be your response unless you have a particular disinterest or unliking of sports