One of the nation’s oldest and most venerated Latino civil rights organizations is at a critical juncture that some members say could determine its direction — or have dire implications for its future.

A messy legal dispute, rooted in a decades-long debate over whether Puerto Rico should become a state, has led to infighting among the members and leadership of the group, the League of United Latin American Citizens, known as LULAC.

Some have accused its president of fueling the very discrimination the organization first set out to eliminate. Half a dozen current and former members contend that Domingo Garcia, a Dallas lawyer who has led the group since 2018, is seeking to marginalize Puerto Rican members after he almost lost his seat last year to a candidate of Puerto Rican origin.

They said the organization had suspended Puerto Rican members and fired, without cause, some of its most prominent leaders of Puerto Rican descent. Two amendments to the group’s constitution are up for consideration, one of which threatens to purge all island residents from its ranks.

LULAC has become instrumental in turning out the vote in Democratic politics, as most Latinos have historically tended to lean Democrat. The civil rights organization will be among major Latino advocacy organizations looking to play a pivotal role in the 2024 presidential election as Latinos have emerged as important swing voters.

They are now one of the fastest-growing and quickly diversifying racial and ethnic voting blocs in the United States. An estimated 34.5 million Hispanic Americans were eligible to vote in the 2022 election alone.

Next month, the organization is set to hold its national convention in Albuquerque, N.M., and some members worry that the tension may feed into historical perceptions of a division between Mexican Americans in the Southwest and Puerto Ricans on the East Coast. There is also concern that the amendments could empower a small clique within the group who have long sought to shut out its Puerto Rican members.

Others argue that the infighting could distract from the issues they say should be front and center for the organization, such as increasing access to education or the lingering effects of the pandemic on Latinos, among the hardest hit by the health and economic crises.

Founded in 1929 in South Texas by a group of mostly Mexican American veterans of World War I, LULAC has weathered bitter infighting before. Early on, its founders limited group membership solely to U.S. citizens, barring undocumented workers and Mexicans in the borderlands who sought to join.

At its founding, the group worked to expand Hispanic civil rights at a time when Texas Rangers would set up blockades to intercept Mexican American organizers and signs outside some restaurants still read “No Mexicans or dogs allowed.”

From a small network of local groups, LULAC rose to national prominence, winning legal battles to desegregate and better integrate public schools and promote homeownership and economic mobility for a younger generations of Latinos. The group was part of a successful effort to end segregation in California’s public schools, which paved the way for the landmark Supreme Court ruling in 1954 that found segregating children in schools by race was unconstitutional.

As the group gained influence and expanded its reach, rifts developed among its membership. Latinos, once often seen as a monolithic group, have grappled in recent years with questions about political and cultural identity, as they have become the second largest ethnic voter bloc behind white people. The suspensions and proposed changes to the organization’s constitution could be a harbinger for its future.

The first proposed amendment would rewrite a provision in the constitution to limit group members to residents of the United States of America, “meaning the 50 states and the District of Columbia” — but not Puerto Rico. If that fails, another would mandate that Puerto Rican membership be proportional to the Puerto Rican population in the United States.

Carlos Fajardo, whose position as Puerto Rico LULAC state director is in limbo — the group said he was among Puerto Rican leaders “currently suspended” — called the suggested amendments “bigoted” and “the latest act of discrimination” against Puerto Ricans.

“It is sad,” Mr. Fajardo said, adding that the group’s president had also done a lot for Puerto Ricans, who were accepted into the group more than 30 years ago. “We are having to fight for our civil rights within a civil rights organization.”

Joe Henry, who is the group’s state political director for Iowa and Mexican American, said it did not make sense for the organization to exclude residents of Puerto Rico, who are American citizens. He argued that such a move would run counter to the group’s spirit and mission. “Our organization is about — an injury to one is an injury to all,” Mr. Henry said.

Mr. Garcia, the group’s president, who is also a Mexican American, rejected the claims of discrimination.

“No such thing,” Mr. Garcia responded in an interview when asked about claims that he was trying to limit the power of Puerto Rican members. He said the issue was that organization had not been able to confirm whether the group’s councils in the territory had been funded by a political party, which could jeopardize its status as a nonprofit.

“We have had Puerto Rican councils for 30 years, it has never been a problem,” he said. “This is only an issue of where the funding comes from.”

Amendments to the group’s constitution have rarely been approved, Mr. Garcia and other leaders said, requiring a two-thirds vote from all registered delegates present at the national assembly. The group has about 132,000 members and supporters in the United States and Puerto Rico, but not all attend its conference.

Mexican Americans and Puerto Ricans historically have composed the two largest Latino subgroups in the United States, with Mexicans and Mexican Americans accounting for nearly 60 percent of the Latino population, or about 37.2 million people, according to the Pew Research Center, more than four times the number of people of Puerto Rican origin.

The tension within LULAC started to build last year when hundreds of members gathered in Puerto Rico for the group’s 2022 conference. The event was brought to a halt abruptly, the night before group’s elections, including a contest between Mr. Garcia and Juan Carlos Lizardi, the son of Elsie Valdés, a longtime board member and Puerto Rico statehood activist.

A Texas judge ordered the organization to pause its proceedings after five leaders filed a lawsuit in Dallas County against the group’s board members, arguing that the New Progressive Party in Puerto Rico had been working with LULAC insiders like Ms. Valdés to sway the election outcome. After being informed that the conference was suspended, about 900 members still gathered in Puerto Rico and held a symbolic voice vote in support of Mr. Lizardi.

Bernardo Eureste, who drafted the amendments that seek to deny Puerto Rican residents membership, said the proposal only sought to clarify what was already in the group’s constitution and to stop what he said was “a takeover” of the organization.

When asked if the amendments went against the group’s spirit of unity, as some members claimed, he responded: “Were you sent to me by the Puerto Ricans? Or the people from the mainland?”