Nearly half of Americans support banning Nazis and white supremacists from speaking on college campuses, a poll shows, but higher education critics warn that such a move would be imprudent and legally dubious.

The poll was sponsored by the documentary “No Safe Spaces,” featuring comedian Adam Carolla and radio host Dennis Prager on a tour of U.S. universities, and asked respondents to choose from a list of 12 groups that should not be allowed to speak on college campuses.

Forty-eight percent chose Nazis, 40 percent white supremacists, 32 percent Holocaust deniers and 24 percent communists.

Mr. Prager said the results demonstrate America’s increasing antipathy for the right of freedom of speech guaranteed in the First Amendment.

“The whole point of our Constitution, and of America itself, is that all speech — especially hate speech — is protected,” Mr. Prager said. “After all, love speech needs no protection. It’s precisely offensive speech that our founders intended to protect and that we are compelled to defend. I decided to participate in this film because if we don’t get this right, we will literally lose our country and our freedoms.

“Sadly, this poll reinforces the need for the film and for us to save our country from tyranny.”

Compared with the general public, millennials are only slightly more in favor of prohibiting people with unpopular beliefs from speaking on college campuses. Fifty percent of the up-and-coming generation said Nazis should not be permitted to speak at universities, compared with 48 percent of Generation X, 47 percent of baby boomers and 44 percent of those 72 and older.

Communism was the only ideology that millennials supported significantly more than their elders. Just 18 percent of millennials said proponents of communism should be barred from speaking on campus, compared with 26 percent of Gen X, 26 percent of baby boomers and 31 percent of the older generation.

Six percent of millennials and 6 percent of all respondents said political conservatives should be shunned from academia.

Peter Wood, president of the National Association of Scholars, said the poll may understate support for banning conservative speakers from college campuses. He said it’s not uncommon for those on the right to be branded as Nazis or white supremacists when they attempt to deliver lectures at colleges and universities.

Last month, for instance, protesters at the University of California Berkeley greeted Daily Wire editor Ben Shapiro, an Orthodox Jew, with chants of “Nazi, go home!”

“I suspect that the term ‘Nazi’ is received as having a much broader applicability than is appropriate,” Mr. Wood said. “Lots of people who may rightly be seen as on the political right are caricatured as Nazis.

“Nonetheless, banning Nazis is not consistent with the First Amendment and probably not consistent with most understandings of academic freedom,” he said.

Support for viewpoint-based censorship is influenced by educational attainment, the poll found. Respondents with some college or graduate school education were more likely than those with a high school degree or less to say unpopular beliefs should be cast from college campuses.

Overall, 48 percent of respondents said, “Any group, no matter how controversial, should be allowed to speak on campus.”

Other polls support the notion that a significant percentage of Americans favor restrictions on speech they don’t like.

A Brookings Institution poll in September found a plurality of Americans, 44 percent, said the Constitution does not protect hate speech, compared with 39 percent who said it does and 16 percent who said they don’t know.

It’s one of the trends filmmakers are trying to expose in “No Safe Spaces.”

Set for release in mid-2018, the documentary will feature interviews with students and professors about illiberal tendencies in higher education, as well as footage of Mr. Carolla and Mr. Prager attempting to navigate the protests, riots and barricades that inevitably accompany conservatives who attempt to speak on college campuses.

The two initially were barred from an appearance at the University of California-Northridge. After lawyers intervened on their behalf, they delivered the lecture without further incident in February.

Mark Joseph, producer of “No Safe Spaces,” said conservatives and liberals have come to realize that free speech is under fire in academia.

“We’ve interviewed a number of people across the political spectrum for this movie,” Mr. Joseph said, “and from Van Jones to Jordan Peterson, and Everett Piper to Alan Dershowitz, a consensus is emerging that free speech is under attack, and this poll confirmed that.”

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