The controversy over Ms. Sarsour’s appearance is the latest dispute in a heated national dialogue over free speech on university campuses.

But in this instance, the roles have been reversed. Other protests have largely pitted left-wing students against conservative speakers like Mr. Yiannopoulos, Ann Coulter, Gavin McInnes and Charles Murray. This time, conservatives are leading the charge against Ms. Sarsour.

Her critics are a strange mix, including right-leaning Jews and Zionists, commentators like Pamela Geller, and some members of the alt-right.

They accuse her of sympathizing with terrorists, supporting Sharia law and anti-Semitism for statements she has made about politics in the Middle East.

The CUNY chancellor, James B. Milliken, has defended the appearance on the basis of free speech, and a group of CUNY professors, some prominent progressives and liberal Jewish groups have spoken in her support.

Fred Smith Jr., a constitutional scholar and assistant professor at the University of California, Berkeley School of Law, said the controversy was a reminder of the bipartisan nature of the outcry over free-speech issues.

“There are a few people who have been very effective in branding the left at shutting down free speech, but the moment they are confronted with leftist speech they don’t like, they are equally outraged and poised to suppress that speech,” he said. “I don’t think that’s the answer for either side. The more you try to suppress speech, the more the ideas of the suppressed speaker become salient to more people. It makes the person more well known and attracts more people to those ideas.”

The debate about Ms. Sarsour’s speech began last month with Dov Hikind, a conservative Democratic state assemblyman who represents a largely Orthodox community in Brooklyn. Mr. Hikind said Ms. Sarsour should not have been chosen, pointing to her recent appearance in Chicago with Rasmea Odeh, who was convicted in Israel of playing a role in the bombing of a supermarket that killed two civilians in 1969.

Mr. Hikind also pointed to a picture Ms. Sarsour once posted on Twitter of a Palestinian boy standing across from police officers with rocks in his hands. Ms. Sarsour wrote that the photo was “The definition of courage.”

Mr. Hikind said in a phone interview, “You can’t support a terrorist and then be the commencement speaker at a university that my taxes help pay for.”

His opposition drew a flurry of coverage in late April, as news that Ms. Sarsour had been invited to speak spread among local news outlets, Jewish publications and the conservative media establishment. Mr. Hikind’s office also circulated a letter signed by 100 holocaust survivors asking Gov. Andrew M. Cuomo to cancel the address.

Unlike some controversies over Israel that have occasionally split New York liberals, this one seems to have united many progressives behind Ms. Sarsour. A coalition of groups rallied in front of City Hall this month to support her right to speak.

Brad Lander, a Democratic city councilman from Brooklyn, described the accusations against Ms. Sarsour as “preposterous,” and pointed to her help in raising money to repair two Jewish cemeteries that were vandalized in St. Louis and Pennsylvania in February.

“She’s been in my synagogue,” he said. “She and my rabbi are friends. There’s no doubt that part of what this is is backlash against the idea of having a Palestinian-American as a visible leader and inheritor of the civil rights movement.”

He added, “One terrible feature of the Trump regime is that it threatens to tribalize all of us.”

At the protest, even Mr. Yiannopoulos briefly acknowledged Ms. Sarsour’s right to speak, before making a racially tinged joke about her getting paid in goats. He was more restrained in an emailed response to a question.

“Unlike some of the other speakers, I don’t want Sarsour canceled,” he wrote. “I want as many people as possible to hear her odious thoughts. That doesn’t mean I can’t explain why she is dangerous and wrong.”

Ms. Sarsour said she had nothing to apologize about for her views.

She said there were questions about the integrity of Ms. Odeh’s conviction many decades ago. The photo of the Palestinian boy was taken during a week when about 200 Palestinians had been killed, she said. And she said she had never planned to speak about Israel in the commencement address.

Ms. Sarsour said she believed she became a target for far-right conservatives in the days after the Women’s March, which she said was evidence of a larger “Islamophobia industry.”

She has hired two private bodyguards to accompany her to public events. She says she regrets that she has not been able to shield her three children, all teenagers, from the vitriol and threats she has received online. Still, she said, she does not plan to be silent.

“I’m Muslim, I’m Palestinian, I’m a woman in a hijab,” she said. “I’m everything they stand against.”

She added, “I have a bigger mission here.”