Protesters shout Thursday to drown out a speech by white nationalist Richard Spencer, appearing before a mostly empty venue at the University of Florida in Gainesville. (Evelyn Hockstein/For The Washington Post)

When the posters went up a third time, it happened in broad daylight, midmorning on a Thursday. Rabab Abdulhadi saw the move as increasingly bold and deeply unsettling.

There was her face, and the names of her students, again plastered all over campus below these words: "TERRORIST SUPPORTERS."

Abdulhadi is San Francisco State University's sole Arab Muslim professor teaching at its College of Ethnic Studies. She is a frequent target of right-wing groups because of her criticism of Israel.

While there is no evidence that the posters' message has any validity, Abdulhadi was incensed, and she looked to the university to do something about it. University administrators, however, said the posters' makers were entitled to free speech.

"I am 100 percent in favor of the First Amendment," said Abdulhadi, a short 62-year-old with cropped hair and an Arabic accent. "It's a question of when does speech become an incitement to violence?"

The nation's colleges are facing growing pressure to redefine the limits of free speech in an age of resurgent white supremacists and amid pleas for inclusiveness on increasingly diverse campuses. For some students and professors, suppressing hate speech has become more important than protecting the values enshrined by the First Amendment.

That conflict was on display last week when hundreds of protesters at the University of Florida drowned out a speech by white nationalist Richard Spencer, prompting him to leave the stage early.

[A white nationalist is coming to campus. Florida prepares as though for a disaster.]

It hasn't always been this way. During the Vietnam War, for example, it was more often students who were pushing administrators for greater freedom of speech.

But today's college students, as well as many professors, have grown increasingly intolerant of views they find offensive, said Geoffrey Stone, a professor of law at the University of Chicago. It's a trend that he said has picked up in the past few years, and there are a range of factors at play.

For one, colleges are more diverse, giving greater voice to minority students who suffer discrimination. Social media and divisive politics have also made hateful speech more pervasive.

More than half of today's students say that it's important to be part of a campus community where they are not exposed to intolerant or offensive ideas, according to asurvey by the Foundation for Individual Rights in Education. The results were even more pronounced for those who aren't white: More than three-quarters of black students and more than two-thirds of Latino students agreed with that idea.

The notion that hate speech should be suppressed is increasingly prevalent. Only about a third of students in the survey said hate speech should be protected by the First Amendment. Almost half say it should not protect hate speech at all.

While some hate speech — typically that which involves a direct threat or incitement to violence — is illegal, most, including vocal racism and personal insults, is not.

Even so, fliers and chalkings reading "hate speech is not free speech" have become a common sight on quads and campus bulletin boards this year, as they are at San Francisco State, even as campus administrators gently push the opposite line.

Suzanne Goldberg, a law professor and Columbia University's vice president for university life, sent a message to the campus community urging respect for a planned speech by a controversial figure — far-right British activist Tommy Robinson, who argues that mass immigration has led to "the fall of Europe."

[A brief history of Donald Trump’s mixed messages on freedom of speech]

While the university's values reject white supremacism and anti-Muslim sentiments, "it is foundational to Columbia's learning and teaching missions that we allow for the contestation of ideas," Goldberg wrote. "This includes expression of ideas that are deeply unpopular, offensive to many in our community, contrary to research-based understandings, and antagonistic to University tenets."

Robinson's video talk was interrupted anyway, as students shouted and held signs that said "White silence = compliance" and "United against Islamophobia."

At San Francisco State, the free-speech debate has centered on a long-brewing contest of campus activism between what could be loosely called the "pro-Palestine" camp and the "pro-Israel" camp. What has long been a hot-button issue on that campus has escalated, with filed grievances, a lawsuit and donors threatening to withhold funds.

The "terrorist" posters by the David Horowitz Freedom Center — an outside group known for assailing students and academics who criticize Israel — is only the latest in a string of events that have raised questions about what speech is protected and what isn't.

Last June, three Jewish students and three Jewish community members sued university administrators and Abdulhadi, who sponsors a Palestinian student group and teaches classes on Arab identity, accusing them of fostering anti-Semitism on campus.

The lawsuit filed by the Lawfare Project, an organization self-described as "the legal arm of the pro-Israel community," focuses heavily on campus speech — equating anti-Israel rhetoric with anti-Semitic rhetoric and arguing that there should be no place for anti-Semitism on a university campus. One of the key incidents the lawsuit cites is a 2016 speech by a hard-line Israeli politician, an event quickly shouted down by pro-Palestinian activists.

[Sessions criticizes U.S. universities for their free-speech policies]

"Contemptible speech and expression at SFSU often makes Plaintiffs feel uncomfortable and vulnerable," the lawsuit says. The plaintiffs don't want to suppress "this vile speech," it says. "They simply want to be guaranteed the same inherent rights to speak, listen and assemble" that other members of the campus are afforded.

The challenges for university administrators have yielded no consensus on solutions, particularly as they face pressure from donors to show no tolerance for hate speech that allegedly targets Jewish students and from Palestinian students who accuse administrators of pandering to Islamophobia.

"We talk a lot about how we want our students to feel happy, safe and well when they're at college. So I think in some ways we've set up this idea that it's a safe space," said Mary Ann Begley, San Francisco State's interim dean of students. "Maybe what we haven't done as well is, when these tough conversations happen, how we're going to have those conversations and how we're going to heal as a community."

The question of what qualifies as hate speech has compounded the argument over whether it should be tolerated.

The posters that San Francisco State administrators considered protected were seen as incitement in the eyes of Abdulhadi and her supporters. And she said they made her feel unsafe on campus.

The Jewish plaintiffs in the lawsuit say the anti-Israel chants that drowned out the Israeli politician made them feel unsafe and amounted to anti-Semitism. Abdulhadi's students, in turn, say that branding the critics of Israel's human rights abuses as anti-Semites is, itself, inherently Islamophobic and anti-Arab.

It's unclear where exactly the university stands.

[A university president held a dinner for black students — and set the table with cotton stalks and collard greens]

University President Leslie Wong, who is named in the lawsuit, said in a recent interview that anti-Semitism on campus has been "the biggest issue over the past few years." But he declined to comment further because of the impending lawsuit.

Wong launched a task force to address issues of "campus climate," including anti-Semitism and Islamophobia. He said administrators are also talking to students about the meaning of free speech.

It might be an uphill battle. The prevailing opinion among the most vocal members of both camps seems to be that offensive speech or actions qualify as hate speech and that hate speech is something to be regulated.

For example, Jacob Mandel, a recent San Francisco State graduate and one of the plaintiffs in the lawsuit, described the university's decision to forge a relationship with a Palestinian university, An-Najah, as threatening enough to warrant mention in his lawsuit against the university, alleging anti-Semitism.

"Once I found out that the university had established a relationship with An-Najah, I felt nervous and scared," he said.

Ollie Benn, the executive director of Hillel, a campus Jewish organization, described the anti-Semitism as part of the campus atmosphere. "Unless a student sort of declares that they're anti-Israel, they're sort of shunned from participation in discussions of social justice and things that have nothing to do with the Middle East," said Benn, who is not a plaintiff but is quoted in the lawsuit in support of its claims.

A 22-year-old member of the General Union of Palestine Students (GUPS) said the same is true for her when certain speakers such as the Israeli politician come to campus.

"It's triggering for us," said the student, who also thinks that other symbols of "violence" — including U.S. military members and Trump administration officials — should be excluded from campus.

"In what sense should we allow an administration that is racist, that has set bans on our communities, to be allowed into campus?" said the student, who asked that her name be withheld because she fears ending up on a poster like the one that targeted Abdulhadi and her classmates.

Abdulhadi says it's an imbalance of speech, rights and resources that justifies one side's arguments and not the other's. Only one type of hate speech, she argues, appears to pose a red line for administrators, and it's anti-Semitism, not Islamophobia.

"Any time you say 'anti-Semitism,' whether it is real or fake — like the kid who called [in bomb threats to] all the JCCs — people get scared. It has a chilling effect," Abdulhadi said.

The university says that it treats both anti-Semitism and Islamophobia as problematic issues that warrant attention.

Abdulhadi says she believes that anti-Semitism exists; sometimes she has to correct students to say "Israel," and not "the Jews" when they're talking about the Jewish state. But she maintains that there is an imbalance in whose freedom of speech is allowed, says Abdulhadi, who grew up under Israeli occupation.

"When we talk about freedom of speech — not everybody's freedom of speech is equally accessible because we don't all come from equal places," she said. "We are being silenced."

Correction: A previous version of this story mischaracterized Rabab Abdulhadi as the only Arab Muslim professor teaching about Arab and Muslim issues at San Francisco State University; she is the only Arab and Muslim professor teaching at the College of Ethnic Studies. The article also mischaracterized Mary Ann Begley as the dean of student affairs; Begley is the interim dean of students. The article misspelled An-Najah National University.