Already the target of a federal lawsuit, a controversial Arizona law that essentially bans ethnic studies in public schools has pitted the largest school district in Tucson against students, parents, and other program supporters.

Hundreds of people converged Tuesday on the Tucson Unified School District headquarters to hear the governing board discuss possible changes to the district’s Mexican-American history and culture program.

Following a raucous four-hour meeting punctuated by the removal of several people from the boardroom and loud protests from the crowd, the board postponed taking action until after it convenes a public forum on the matter.

The law in question, which took effect Jan. 1 and is known as HB 2281, bans ethnic studies that promote the overthrow of the United States government and resentment toward a race or class of people. Also outlawed are classes designed primarily for students of a particular ethnic group and those that advocate ethnic solidarity rather than the treatment of students as individuals.

Tom Horne drafted the law when he was superintendent of Arizona schools. Just before he stepped down from that post to become the state’s attorney general, he found the Tucson district’s classes out of compliance with the law. The district could lose millions of dollars in funding.

The new Arizona schools superintendent, John Huppenthal, is expected to rule on whether the Tucson district’s Mexican American Studies program is in compliance with HB 2281.

In the meantime, the Tucson district has proposed changing the program. Currently, Mexican-American courses can help satisfy the social-studies requirement for graduation (although students don’t have to take the courses to fulfill the requirement). Under the proposal, the Mexican-American classes would not count toward the social-studies requirement and would instead be electives. Six-and-a-half elective credits are needed for graduation.

“There’s been a sense in the district that the Mexican American Studies program is flawless, and despite its positive qualities, this rhetoric doesn’t serve the district well,” said Mark Stegeman, the board president seeking to modify the classes. “Almost all of our programs have some room for improvement.”

Program supporters describe ethnic studies as crucial to closing the student achievement gap among an underserved population. The supporters point to data indicating that students who take the ethnic studies classes are more likely to go on to college. The district has more than 50,000 students, about 60 percent Hispanic.

At the meeting Tuesday, Sean Arce, director of Mexican American Studies, told board members that making the courses elective would essentially kill the program. The move would eliminate student incentive to enroll in the classes, he said

“Students, particularly Latino students who have traditionally struggled to graduate, will not take the additional courses and double up for an additional history class,” he said.

Mr. Arce is one of several plaintiffs challenging the law in court on the grounds that it violates the First and 14th Amendments, which guarantee free speech and due process, respectively.

During the session, speakers chastised board members time and again, saying the district’s top policymakers are caving to the politics of Mr. Horne, the former state superintendent.

“You are being the lackey of Tom Horne,” longtime activist Salomón Baldenegro told the board.

But Nina Samuels, a Peru native, said she did not expect the board to educate her children about her ethnic background.

“I myself, with my husband, taught our children where I come from, my customs, my Spanish language, my foods, all of that,” said Ms. Samuels, who was applauded by some and jeered by others.

Dozens of police, some in riot gear, surrounded the building where the meeting (which included an overflow crowd) took place. A police helicopter even hovered above. Before the start of another meeting last week, when the matter was originally supposed to be taken up, youths had chained themselves to board members’ chairs. That session was canceled.

On Tuesday, some attendees emphasized they’d be taking a less belligerent approach.

“We’re not trying to start a riot or anything like that,” said Marcella Marin, a former ethnic-studies student who is now a sophomore at the University of Arizona in Tucson.

“It’s more about the power of change,” added Ms. Marin, who wore a white shirt scribbled with the words: “You may silence my voice but never my spirit.”