A member of the black student protest group Concerned Student 1950 addresses a crowd at the University of Missouri in Columbia after the announcement Monday that system President Tim Wolfe would resign. (Jeff Roberson/AP)

College campuses across the country have plunged into an intense debate that pits free-speech advocates against those who want to rein in insults, slurs and other offensive expressions.

Student uprisings at Yale, the University of Missouri and elsewhere show a passionate desire to confront racism and bigotry in all its forms, from the disgustingly overt — a fecal swastika smeared on a bathroom wall in Columbia, Mo. — to the subtle or even unintentional offenses known as “micro-aggressions.”

But the drive to combat hurtful and hateful speech is colliding in some places with principles that educators have long held dear: freedom of speech and academic expression. Universities are struggling to strike a balance as they seek to foster a climate that is at once tolerant of racial and cultural differences but also unafraid of a robust clash of viewpoints.

“Every college president faces a challenge in creating a welcoming and productive environment but at the same time encouraging the free exchange of ideas,” said Terry W. Hartle, senior vice president of the American Council on Education. “A lot of ideas can be very unwelcoming. How you handle those is something that a lot of people worry about.”

On Tuesday evening, Yale officials addressed the debate head-on. They told the university community that they embrace the school’s diversity and want to ensure that all groups are treated with respect. But they also emphasized the centrality of speech on the Ivy League campus.

Yale students march in New Haven, Conn., on Monday in solidarity with minority students who are decrying racism on campus. (Isaac Stanley-Becker/For The Washington Post)

“We also affirm Yale’s bedrock principle of the freedom to speak and be heard, without fear of intimidation, threats, or harm, and we renew our commitment to this freedom not as a special exception for unpopular or controversial ideas but for them especially,” Yale President Peter Salovey wrote in a joint statement with a dean.

Many academics are heartened that students from minority groups feel emboldened to speak out forcefully against indignities they have suffered quietly for generations. The abrupt resignation Monday of the University of Missouri System’s president — amid pressure from civil rights protests over his response to troubling racial incidents at the school — showed the surging power of these student voices.

Derald Wing Sue, a professor of psychology and education at Teachers College at Columbia University, said events in Missouri showed the results of students’ pent-up frustration at having to routinely endure insulting expressions of bias. “It is cumulative,” Sue said. “Years of being discriminated against, being fatigued and tired of having to take it.” A racial epithet or a swastika, in that environment, he said, can be “the match, the spark, that creates the explosion.”

Others fear that colleges are jeopardizing freedom of expression, including the freedom to make verbal mistakes, a core academic value. Robert Shibley, executive director of the Foundation for Individual Rights in Education, said he worries about a rising tendency toward censorship on campus. Shibley cited the rapid expulsion of two University of Oklahoma students in March after they participated in a fraternity’s racist chant, captured on a video that went viral online.

“Anytime someone is punished for pure expression, that is an attack on the principles of free speech,” Shibley said. “It’s not the government’s job to pick what speech is good and what speech is bad. We’ve always said the remedy for bad speech is more speech.”

University of Maryland President Wallace D. Loh faced a similar situation in March when the school learned about a racist, sexist e-mail a student had sent to members of his fraternity. Loh met with the student, and accepted his apology and decision to leave school for the semester. But Loh and other U-Md. officials concluded that the e-mail, “while hateful and reprehensible, did not violate university policies and is protected by the First Amendment.”

Loh asked the community to forgive the student and start a dialogue to improve the campus climate in College Park.

“We have a responsibility to advance the values that define a community,” Loh said Tuesday. “We have to take affirmative steps in education and outreach before these incidents happen.”

Schools nationwide, public and private, have grappled recently with controversies about speech and expression. Some critics wonder whether colleges have become too politically correct, obsessed with preventing “micro-aggressions” and promoting “trigger warnings” and “safe spaces” — a view expressed in a recent article in the Atlantic headlined “The Coddling of the American Mind.”

The University of Illinois at Urbana-Champaign last year rescinded a job offer to a professor, Steven Salaita, after critics took offense at the tone of comments he made about Israel on Twitter. The American Association of University Professors later censured the school for breaching principles of academic freedom.

Williams College in Massachusetts was roiled last month after a student club, called Uncomfortable Learning, invited author Suzanne Venker to speak. Many students objected, citing what they saw as Venker’s rejection of feminism. Reaction was so intense that students canceled the event, concerned for her safety. A student then reinvited her, but she declined.

At Wesleyan University in Connecticut, the student newspaper, the Wesleyan Argus, faced a sharp backlash in September after publishing an opinion piece critical of the tactics of the Black Lives Matter movement. The student government later took steps toward cutting the newspaper’s budget for next year.

Rebecca Brill, the twice-weekly paper’s co-editor-in-chief, said she drew two lessons from the episode: that student journalists must listen closely to their community if their work causes an uproar and that free speech is essential to the dialogue.

“This is clearly a nuanced issue,” Brill said. “I would never want to be totally blind to the hurt that the op-ed caused some students.” But the 21-year-old senior from New York added that the piece spawned “interesting and productive” conversations on campus.

“It is a dangerous precedent to try to silence a voice you don’t agree with,” Brill said. “We need to be able to say what we think about issues we’ve given thought to.”

Michael S. Roth, Wesleyan’s president, declared support for free speech after the episode.

“The institution has to protect people against attack that causes harm,” Roth told The Washington Post. “But it should never protect people against ideas that are difficult to digest.”

At Yale, two recent incidents touched off protests late last week. Students alleged that fraternity brothers turned black women away from a party, saying, “White girls only,” a claim the fraternity’s president has denied. The university is investigating the incident.

And a faculty member who lives in one of Yale’s residential colleges wrote an e-mail raising questions about a message from school officials that urged students to consider whether their Halloween costumes might offend someone by stereotyping a culture or race.

“I don’t wish to trivialize genuine concerns about cultural and personal representation,” wrote Erika Christakis, an early-childhood educator. She is the wife of Nicholas Christakis, the Silliman College master. She added: “Nicholas says, if you don’t like a costume someone is wearing, look away, or tell them you are offended. Talk to each other. Free speech and the ability to tolerate offence are the hallmarks of a free and open society.”

The two defended the e-mail later on social media, but their comparisons to debates about free speech and “trigger warnings” only made students angrier.

Many students gathered outside the main library to write messages in chalk. When the first black dean of Yale College walked up, they surrounded him in a remarkable, sometimes tearful, sometimes angry conversation, with the crowd swelling to more than 100. The dean, Jonathan Holloway, mostly listened. The next day, he sent an e-mail that read, in part: “Remember that Yale belongs to all of you, and you all deserve the right to enjoy the good of this place, without worry, without threats, and without intimidation.

“I don’t expect Yale to be a place free from disagreements or even intense argument; I expect you to disagree on a wide range of issues. In so many ways, this is the purpose of our institution: to teach us how to ask difficult questions about even our most sacrosanct ideas.”

At Missouri, protesters angered by racist, anti-gay and anti-Semitic incidents on campus — and what they felt was an inadequate response from administrators — exerted enough pressure to force the system’s president, Tim Wolfe, to resign Monday. Within hours, the chancellor of the Columbia flagship, R. Bowen Loftin, stepped down as well.

On Tuesday night, the campus reeled from posts on Yik Yak, a social-media app, which included a threat to black students and a post that read, “Well tomorrow Mizzou will really make national news.” MUAlert, the university’s online emergency information center, released a statement saying that the university “is aware of social media threats and has increased security.”

Earlier Tuesday, the campus police sent a message to all students urging them to report immediately all “hateful and/or hurtful speech or actions” they see.

“While cases of hateful and hurtful speech are not crimes,” the message said, if the people involved are students, the university can discipline them.

While many people celebrated the chance to change campus culture and send a strong message that bigotry would not be tolerated, others wondered where and how the line would be drawn for unacceptable speech.

“In the U.S., it is not a crime to be a racist moron. So the university cannot punish students simply for being bigoted,” said Ben Trachtenberg, an associate law professor at Missouri who agrees with the protesters that there are some real problems with race on campus. “So it does create some tension when people say things that are both entitled to First Amendment protection and extremely hurtful. The line between mere bigotry and actual harassment and threats is not always obvious.”

Isaac Stanley-Becker in New Haven, Conn., contributed to this report.