I wouldn't be bothered if my kid did baseball or cricket. Bored, perhaps, but not bothered.
Let's see, espn.com. Hockey can be super violent, but I'm probably ok with it, gotta check the numbers. Golf, boring, whatever. Fighting games - wrestling, MMA, etc, I'm probably ok with after a reasonable age. Certainly I would have no issues taking kiddo to Krava Maga.
(Personally I will go to Sounders (MLS) and Reign (NWSL) games, and I'm curious to see men's gymnastics at U of Washington this fall. It might be just a little Seattle)
e: The "red state" crew are, I think, more comfortable with idea of casual violence (and thus football). It's not as much of a Big Deal to them, often life is more rough and tumble IMO. I grew up in Idaho, so I do have some Life Experience in what I'm saying.
Perhaps it's not a red or blue split, but those sports you listed are definitely on one side of a major class divide. Basketball and football are moving towards the other. And while I understand that a competition between some farm hicks and big-city boys can bring two groups together, access to sports like skiing is fairly exclusive.