A growing group of Columbia University undergraduates are calling for an overhaul to the school’s required reading list and asking whether classics with sexually violent content should bear cautionary notes.

The effort to add “trigger warnings” to texts has polarized universities around the U.S. At the New York City Ivy League school, it is focused on an introductory humanities course, “Masterpieces of Western Literature and Philosophy,” that all undergraduates at Columbia College take.

With school out for the summer, Columbia is making changes to next year’s required reading that reflect some student concerns. Ovid’s “Metamorphoses”—a book students said was potentially offensive because of its sexual violence—is out, and a Toni Morrison novel was added.

But the effort to add trigger warnings has failed.

“At no point did [we] consider trigger warnings as being something that could be productively or intellectually mandated, or made structural,” said Julie Crawford, chairwoman of Columbia College’s literature humanities department.

Such warnings could threaten “intellectual freedom,” Ms. Crawford said.

She said the decision to revise the reading list was unrelated to the student effort to change the curriculum.

The books in the Western literature course wouldn’t appear, at first glance, to be controversial choices: They include Shakespeare’s “ King Lear,” Homer’s “The Odyssey” and Plato’s “Symposium.”

But students said the school is prioritizing an outdated, Eurocentric selection despite Columbia’s diverse student body, mandating works with overtones of racism and sexism and teaching them uncritically. Many of them have said that if the school insists on requiring works depicting rape then those books should come with a warning—either verbally from a professor or stated on the syllabus.

“Some people would prefer not to be blindsided by reminders of traumatic experiences,” said Charlotte Bullard Davies, a rising senior studying political science.

Trigger warnings, she added, “can be a useful tool for someone who says, ‘I am going to read this, but…in a contextualized, thoughtful way.’”

The warnings, depending on who you ask, represent a sign of sensitivity or a threat to open discourse.

At other schools, individual professors have added trigger warnings to some works in the syllabus, at their discretion. But Columbia students have called for more say in the book-selection process, and for trigger warnings as a campus policy.

The debate was laid bare last year in Bwog, a student-run online publication, by three students who questioned the core curriculum. “A university that uncritically accepts rape in its foundational literature class, without any thoughtful discussion...must question its ability to firmly reject rape on campus,” the students wrote.

The piece received hundreds of comments, ranging from “This is ridiculous” to “Is it really out of the realm of possibility…that rape culture is prevalent in our classrooms?”

Miles Hilton, one of the authors, said in an interview: “What we were asking for, more than trigger warnings or diversifying the syllabus, was reframing the way we talk about these books and re-examining the role of the core as an essential part of the Columbia curriculum.”

The piece was followed by forums and other campus discussions on the topic.

In April, another four students wrote an op-ed for Columbia’s college newspaper, the Columbia Daily Spectator, calling for trigger warnings and other changes to the core curriculum, and questioning why the school doesn’t consider modern authors like Ms. Morrison part of the foundational Western canon.

The questions raised by the piece are now “something we talk about every day on campus,” said Ms. Bullard Davies.

“I can understand why students today are sensitive to the fact that this canon represents a particular segment of the privileged population, and I think that’s an appropriate concern,” said Roosevelt Montas, the director of the core curriculum. “But one part of teaching these courses is the story of the uneven distribution of intellectual capital and social power in our history. We look to the past to understand the present.”

Micah J. Fleck is among a group of students who are skeptical about overhauling the core curriculum.

“If you are going to remove some texts, what kind of texts should you replace them with? It would still result in the same goal, which is intellectually stimulating us, and not shielding us from things that might be too scary,” he said. “I definitely am a fan of Toni Morrison’s, but it’s a matter of how well she fits in with the surrounding curriculum, and I hope whoever makes that decision is being intellectually honest.”

Last month, Ms. Morrison’s 1977 novel “Song of Solomon” was added to the required reading list for next year’s students.

Ms. Crawford said the decision was made through a faculty vote. James Baldwin’s “Giovanni’s Room,” and Vladimir Nabokov’s “Lolita” had also been under consideration.

The selections will continue to change, administrators said, but trigger warnings won’t be added.

“One of the great things the humanities do is provide an opportunity, and a venue, to talk about all kinds of things that affect all kinds of people,” Ms. Crawford said. “The classroom is where students are learning how to manage things that have happened.”