Oklahoma’s conservative Republican governor, Kevin Stitt, and its conservative Republican schools superintendent have appeared to stand shoulder-to-shoulder in the years of Donald J. Trump, with the former sending Oklahoma guardsmen to the southern border and the latter stocking the state’s schools with Trump-branded Bibles.

But when the superintendent, Ryan Walters, proposed finding the undocumented students in Oklahoma’s schools, Mr. Stitt said enough is enough.

“When I saw them picking on kids, I thought that’s a step too far,” Mr. Stitt said in a recent interview in his office in the State Capitol.

In an era of anything-goes politics on the nation’s right, the fight in Oklahoma may suggest there is an outer limit to what is acceptable, even for conservatives. Or it could offer a preview of the next frontier in the nation’s battle over immigration.

“It’s incredibly unfortunate that the governor has decided to undermine President Trump’s immigration agenda and take these type of swipes at him,” Mr. Walters said. “He’s attacking President Trump.”

It began when Mr. Walters, the state’s elected superintendent of schools, proposed new rules that would require Oklahoma public schools to collect citizenship information from students. The proposed rules were approved by the state school board in January, and they are now being considered by the Oklahoma Legislature.

But Mr. Stitt, no softy on immigration, lashed out immediately. He soon named replacements to the school board, whose members are appointed by the governor, so he could better resist proposals from the schools chief.

Mr. Stitt has been a strong proponent of border security, sending troops to help patrol the Texas border and lining up to support Mr. Trump’s deportation efforts. But in going after school children, Mr. Stitt said that Mr. Walters — a former high school history teacher who was once a protégé of the governor — crossed a line.

“I’ve never heard Trump talk about, ‘Hey, we’re going to go after kids,’” Mr. Stitt said.

Mr. Stitt, who is in his final term as governor, said he had spoken with Mr. Walters and tried to talk him out of it. “You’re just trying to make a political statement, trying to get your name in the paper,” Mr. Stitt said he told him. “That’s why people hate politicians.”

Mr. Walters, who has been mentioned as a potential candidate for governor next year, has not wavered.

In his office in the state education building, he argued in an interview that his approach closely aligned with the thrust of Mr. Trump’s policies, such as ending automatic citizenship for nearly every person born on U.S. soil and allowing federal immigration agents to enter schools. An attack on the citizenship proposal, he said, was akin to an attack on the president.

Mr. Walters’s goals seem contradictory. Gathering data on the number of migrant students in Oklahoma schools would help provide language services, he said. But he also said he wants to better calculate the cost of undocumented students to state taxpayers.

“My concern are the taxpayers, the citizens of the country and of Oklahoma,” he said. “Those are the people that are here legally, that voted in the elections, that need to be protected.”

His office estimated around 5,000 migrant students attend state public schools, at a cost of about $200 million a year.

Bills in several state legislatures, including in Texas and New Jersey, echo Mr. Walters’s efforts, as they seek to allow schools to collect tuition from migrant students.

Such legislation, which would probably be challenged in court, appeared to be aimed at challenging the core of a 1982 U.S. Supreme Court decision that said states could not prevent undocumented children from attending public schools. That ruling has been a target of some Republicans in recent years, particularly as the balance of power on the Supreme Court has shifted in favor of conservatives.

Mr. Walters said he favored overturning the precedent. Mr. Stitt said he did not.

Jackson Lahmeyer, a pastor in Tulsa, Okla., and member of Mr. Trump’s newly created White House Faith Office, said he liked both the governor and the school superintendent, but sided with Mr. Walters on collecting citizenship data.

“This is the agenda of the president who won,” said Mr. Lahmeyer, whose church has attracted members of Mr. Trump’s family and administration. “We need to know if students are U.S. citizens or if they’re not.”

The governor said he did not object to enforcing immigration law but worried that undocumented parents would potentially keep their children home, rather than be forced to disclose their immigration status.

“The kids didn’t do anything wrong, is my point,” he said.

Mr. Stitt, a mortgage company entrepreneur who was first elected in 2018, suggested a better solution involved fixing the immigration system — an idea that hearkened back to the pre-Trump Republican Party of George W. Bush — so that companies who want to sponsor foreign workers could legally do so more easily.

The Oklahoma citizenship proposal must still be considered by the Legislature before the governor has a chance to formally block it.

Privately, Republicans in the Legislature have chafed at the measure, said Tyler Powell, a Republican political consultant in Oklahoma. Publicly, they have mostly avoided the fray. The leaders of the State House and Senate did not respond to requests for comment.

Mr. Powell said the rightward shift in Republican primaries in 2024 has many were worried about angering Mr. Walters, who is popular with the state’s core Republican base.

“Everyone has a little bit of a fear of Walters,” he said. “Behind the scenes they have ensured that Walters’s policies don’t go through, but they don’t want to come out and walk a plank with their voters.”

Mr. Walters has gained attention nationally for his efforts to introduce religious and Trump-branded conservative instruction into public schools, garnering praise from religious conservatives and those strongly aligned with Mr. Trump. He has moved to purchase Bibles for public schools, to create of a religious charter school and to alter state curriculum to teach the “discrepancies” in the 2020 election, among other things.

“My opinion is Walters needs to stop trying to gain the attention of the president and do his job,” said Mark McBride, a former Republican member of the Oklahoma State House worked on education issues. “I hope that Governor Stitt will continue to push back on the superintendent.”

Mr. Stitt stepped in to replace three members of the State Board of Education in February with new members who would be aligned with him. He said in the interview that he would soon be adding a fourth to fill an empty position, giving him a majority on the board.

Kendra Wesson, an education activist, was one of the board members who voted for the citizenship proposal and was replaced by Mr. Stitt. She said the actual text of the rule — which involved the collection of aggregate data — had been misconstrued by proponents.

“There’s nothing in the rule about going after kids,” she said, adding that it was about helping schools and teachers educate students who arrived speaking different languages. “I feel it is so important to get resources out to them.”

Ms. Wesson said that when the governor called her to tell her he would be replacing her on the board, he offered her a seat on another board. But, she said, it came with an “ultimatum to publicly disavow Ryan Walters.”

A spokeswoman for the governor said Ms. Wesson was never asked to disavow Mr. Walters. Nonetheless, she now serves on an education advisory committee — one that Mr. Walters started.