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.
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.
But certain sports carry too high a risk for me to support my child getting into them before 16ish. They must have a glimmering of a perspective on what life means before choosing to engage in activities that are significantly likely to permanently damage themselves for life. Particularly for football, there are brain effects. Implication here: for boys, football is off the table. For girls, competitive gymnastics. There are likely other sports that could be found as way too high permanent risk.
For perspective on how I'm choosing: soccer is also risky and carries CTE risk, but less so than football. If boy wants to do skiing, running, or mountain biking, that is fine; crossfit, not so much (too aggressive). A certain amount of physical damage is far more acceptable than neurological damage. Things happen though; a friend of mine had his very young daughter fall into a pool and drown a few years after being preemie. That's this life on earth, sorrow and joy. I will give as much responsibility as I can, but the parent's responsibility to is to shape and limit around the ability of the child to react and foresee. Permitting choosing sports which have lifelong damage likelihood, when they are too young to understand the consequences, seems to be poor choice on my part.