Think about smoking or seatbelts. They’re relevant analogies because exhortations to stop smoking and wear seatbelts were once largely relegated to liberal eggheads. As the evidence mounted, though, those causes went mainstream.

Today, it’s clear that a large swath of liberal, college-educated America has changed its mind about the wisdom of playing football. A recent poll conducted by the RAND Corporation for The Upshot asked people about their attitudes toward having their children playing a series of sports. Nationwide, only 55 percent of respondents said they would be comfortable with their sons playing football. The numbers for baseball, basketball, soccer and track were all above 90 percent.

The concerns about football cut across demographic groups, but they were the most intense among Democratic voters who had graduated from college. In fact, the attitudes of three other groups — Obama voters without a bachelor’s degree, Romney voters without one and Romney voters with one — were strikingly similar. Between 58 percent and 65 percent of each said they would be comfortable with their son playing football. Only 32 percent of 2012 Obama voters with a bachelor’s degree gave that answer.

Football was the only sport for which someone’s political views helped predict their comfort level, Katherine Grace Carman and Michael Pollard of RAND noted. Relative to less violent sports, hockey also had a large percentage of people saying they wouldn’t be comfortable with their child playing. But hockey is less popular— and opinions about it didn’t break along partisan lines.

What happens next? The best guess is probably that the future of football will be decided by medical research. It’s now clear that many N.F.L. players are at significant risk of brain damage. But we know less about the risks for high school and youth players, who play less and hit less hard, as Jonathan Chait, himself a liberal, noted in a New York magazine essay, “What Liberals Get Wrong About Football.”