More brands are capturing headlines by tangling with political and social issues in their advertising campaigns. A new poll suggests, however, that most Americans would rather they don’t try the same thing during the Super Bowl. And viewers are likely to get what they want.

Two-thirds of consumers call the Super Bowl an inappropriate place for advertisers to make political statements, according to the poll, conducted online this month by Morning Consult for CMO Today.

“The Super Bowl is definitely the wrong place to make a statement,” said Michael Ramlet, chief executive at Morning Consult, a survey research technology company.

Baby boomers in the poll disapproved of political Super Bowl advertisements more, at 77%, than younger cohorts such as millennials (55%) and Generation Z, defined as those 18-21 years old (43%). But the appetite for big-game politics was smaller than one might expect among young people, who often say they want brands to take positions on important issues. Only 35% of Gen Z respondents to the poll called political Super Bowl ads “very” or “somewhat” appropriate.

“The biggest disconnect between the general public and agencies and companies is this idea that you have to take stands to win Gen Z or millennials,” Mr. Ramlet said. “That’s not what the data shows.”

Newsletter Sign-up CMO Today CMO Today delivers the most important news of the day for media and marketing professionals. PREVIEW

The desire for a politics-free Super Bowl is slightly stronger than consumers’ general preference, at 60%, that brands “stick to what they do and not get involved in cultural or political matters,” according to Morning Consult polling last July. But it may matter more, because marketers during the rest of the year can target their issue-related advertising toward sympathetic demographics. On Super Bowl Sunday, they’ll reach as close to everyone as advertising gets. The 103.4 million viewers who watched in 2018 was a disappointing number by Super Bowl standards but still by far the biggest television audience all year.

Brands should resist the temptation to take on a hot-button issue in the Super Bowl as a way to stand out, said Aimee Drolet, professor of marketing and behavioral decision making at the University of California, Los Angeles’s Anderson School of Management. “It’s generally not the best venue for doing that because the audience is so broad, so invariably you’re going to piss off half the people,” she said.

The Super Bowl has featured political ads before, most notably in the game that took place soon after President Trump’s inauguration, and marketers only have become more politically engaged since then.

Last year’s game was less overtly political, but still included a Coca-Cola Co. ad promoting unity, a diversity theme from T-Mobile USA Inc. and Dodge Ram Trucks using audio of a Martin Luther King Jr. speech in an ad for its Ram pickup truck that promoted public service.

Marketers haven’t shown any inclination to charge into hard-core politics or social controversies during next month’s game, however. Procter & Gamble Co. brand Gillette could have pushed the envelope by bringing this week’s controversial #MeToo-themed spot “We Believe” to the Super Bowl, but a spokeswoman said the brand has no plans to advertise in the Super Bowl this year.

Prior provocateurs such as 84 Lumber Co. and Airbnb Inc., which used the 2017 Super Bowl to run ads taking on President Trump’s immigration priorities, said they are skipping the game again after sitting out last year.

Anheuser-Busch InBev ran an arguably political Super Bowl ad in 2017, featuring the immigrant roots of Budweiser beer, but said any overlap with political arguments of the moment was unintentional. It has promised that its sprawling 5½-minute ad buy in this year’s game will avoid politics.

The poll for CMO Today posed questions about the Super Bowl, advertising and politics to 2,201 adults in a survey that was weighted by gender, race, age, region and education to approximate a target sample, according to Morning Consult, which said the results have a margin of error of plus or minus 2 percentage points.

Write to Nat Ives at nat.ives@wsj.com