Louis Orangeo, 27, a procurement analyst in Bloomfield N.J., did vote for Trump in 2016 and is prepared to vote for him again in 2020, although he isn’t 100 percent sure. Mr. Orangeo said he bought a MAGA hat after the election, “mainly to troll people,” but stopped wearing it because of negative responses. “I hate having to explain it and defend it,” he said. “It always gets a look and a sneer.” He does wear a minor league baseball team’s red cap plenty and nobody has ever said anything.

But Mr. Peterson, the Orlando graphic designer, decided to mothball his red caps after his wife pointed out the potential for confusion or confrontation. And others have made similar decisions after noticing the responses to their red hats.

“One of my favorite hats is a red University of Wisconsin Badgers hat,” said Corey Looby, 31, a database manager from Madison, Wis. “But when I traveled, I would regularly notice glares from people I passed on the street. I don’t want to be associated with MAGA, even mistakenly, so I stopped wearing it.”

The phenomenon is by no means universal; some red-capped fans said the potential MAGA connection had never occurred to them until a reporter brought it up. “I don’t like engaging in political conversations. I just want to be friends and talk about other topics, not politics,” said Jason Stygar, 34, an audio engineer in St. Louis. “But as a lifelong Cardinals fan, I love my red hat — I’ll wear it anywhere and everywhere. It had never even occurred to me, that someone would mistake it for a MAGA hat, and nobody’s ever bothered me about it.”

And some are wearing red caps in defiance, regardless of politics.

“I am not pro-Trump or anti-Trump, but I do have a Detroit Red Wings hat and get weird looks when I wear it,” said Nick Landry, 28, project manager for a carpenter subcontractor in Milford, Mich. “I continue to wear it as a social experiment, hoping people will feel like idiots when they realize that it’s not a MAGA hat and that they’re feeling vitriol over something so stupid.”

Fans and teams alike, though, have long been wary about inadvertent political messaging. In 1954, for example, the Cincinnati Reds changed their official team name to Redlegs, to avoid being associated with the communist scare. (They changed the name back to Reds in 1959.)