There is much more of a relationship between violence and nudity/sex than there is with your example of football and recycling.
Violence and sex are base, essential parts of nature and life, with a long and complicated relationship - one that changes over time.
Through increased education and progressive culture, urges toward violence drop. People tend not to have a caveman-like bloodlust these days, and if they do, it's repressed for the good of everybody else.
Remember that the stereotypical (exaggerated) caveman mating ritual is the alpha male knocks out not only all the other males but also the cavewoman of his choice with a club. Violence (real or threatened) remains a part of sex to this day in many places, and of course plays a big part in history since the caveman days. But in progressive cultures, that is discouraged (to put it mildly) and we try to improve the situation for everyone.
Which takes us back to the strange relationship between violence and nudity/sex in the US. Violence is glorified and widely accepted, and nudity and sex are taboo. Except of course that they really aren't - but there are extraordinarily mixed signals in our culture.
I may not be making myself clear, but the way sex and violence are treated in American culture is significant and says a lot about us as a whole. It's perhaps easier to simply compare to other cultures - consider how these things are considered in the most progressive cultures (Scandinavia etc.) and what we'd consider the least progressive (much of the Middle East, for example), and then figure out where America fits in. It's different, but closer to repressive Middle East cultures than anything even mildly progressive, and IMO it's harmful and stunting our society and culture.