Bo French was such a headache for some Republican leaders last year that they asked him to resign as a county party chairman.

But if their goal had been to try to sideline Mr. French, among the loudest voices on the far right in Texas, that effort may have backfired.

With the support of a couple of billionaire oilmen, Mr. French has become a viable candidate for a powerful statewide job overseeing the Texas oil and gas industry, a cornerstone in the nation’s energy portfolio. Attorney General Ken Paxton headlined Mr. French’s campaign kick off party. Steve Bannon, a former close aide to President Trump, has boosted his candidacy.

On the other hand, Mr. French is opposed by Gov. Greg Abbott and other top Republican officials, along with some of the biggest companies in the energy business. They have all thrown their considerable conservative weight and campaign cash behind Jim Wright, the staid incumbent chairman of the Texas Railroad Commission who is facing Mr. French in a May 26 runoff.

The contest, mostly overlooked outside of Texas, offers a clear test of the power of a traditional business-backed conservative incumbent against a self-described “America First” upstart challenging his own party’s boundaries of decency.

The two men, who have never met in person, are waging parallel but utterly disparate campaigns.

Mr. French, 56, frequently posts anti-Muslim rhetoric on social media, claiming the state of Texas is being taken over by Muslims. He has called for the deportation of nearly one-third of the country and attacked his critics as “liars” or “gay race communists.” Accused criminals, he has said, deserve one punishment: “A rope.”

Mr. Wright has argued that Mr. French’s comments have nothing to do with the job of being an oil and gas regulator — a position that is even more important now as the fallout from the Iran War continues to shock world oil markets.

“Texas needs a workhorse in this position, not a show pony,” Mr. Wright told a small crowd eating fried chicken and mashed potatoes at a country club in Bryan, Texas, last week.

In an interview, Mr. Wright reminisced about growing up in a small South Texas town near a rodeo arena, where he rode bulls. Getting thrown down, trampled, and knocked around will teach you to be resilient, he said, and steer you away from second guessing.

“I’m not the greatest politician in the world by any means,” said Mr. Wright, who was elected in 2020. “But this really isn’t a political office. This is a regulatory office.”

The state’s voters elect three commissioners to serve six-year terms on the Texas Railroad Commission, an obscure but vital state body that regulates oil, gas, pipelines and mining. Its narrow focus and confusing name — which was left over from when it used to oversee rail transport — mean elections to the commission are watched closely by industry insiders.

This year’s Republican primary however, has gained attention beyond the usual circles because of Mr. French’s candidacy.

Mr. Wright, 64, has sought to keep the race narrowly focused on industries the position oversees. At times, Mr. French has successfully pulled him off message, forcing him to weigh in on issues the incumbent says are unrelated to job’s core responsibilities.

Both Mr. Wright and Mr. French say they want to streamline regulations on the oil industry, if elected. While Mr. Wright counts defending private property rights and plugging abandoned wells among his other top priorities, Mr. French wants to use the position to combat the “Islamic invasion of our state” and what he describes as the Chinese Communist Party’s incursions into the energy industry.

Mr. French’s comments have occasionally gone too far for some of the state’s top Republican leaders. Last year, when Mr. French was the chairman of the Republican Party in Tarrant County, he shared a poll on social media asking who was the “bigger threat” to America: Muslims or Jews.

Lt. Gov. Dan Patrick, a conservative Christian who chairs President’s Trump’s Religious Freedom Commission, condemned the poll and called for Mr. French to resign from his party position.

Instead, Mr. French decided to run for statewide office. In podcast interviews, Mr. French, who was raised in the Texas oil country city of Midland and whose family owns a small oil company, described himself as a “business guy” who is speaking out about “the degradation of our society and our culture.”

“I have a track record of being the America First warrior who won’t back down, despite criticism, even from within my own party,” Mr. French said on a recent episode of Mr. Bannon’s podcast. “The establishment does not want me to win this race, so they pulled out all the big guns. They are spending millions of dollars.”

His candidacy has attracted its own megadonors. A political action committee backed by Tim Dunn and Farris Wilks, two West Texas oilmen, has provided about half of the funding for Mr. French’s campaign.

Mr. French has dismissed accusations of antisemitism. He said that last year’s social media poll question, which he deleted, was meant to show Islam “is the bigger threat.”

Mr. French declined a request to attend one of his events, and did not respond to questions about his candidacy.

Mr. Wright has received campaign contributions from political action committees representing most of major oil companies, including ExxonMobil, Chevron and ConocoPhillips.

Mr. French has tried to undercut the incumbent by accusing Mr. Wright of instituting diversity policies and donating to Democrats.

At the campaign stop in Bryan, Mr. Wright was asked to explain.

Pulling out a sheet of paper, he read off prepared remarks. Yes, he donated to his local representative, who is a Democrat. But so are most politicians where he lives in South Texas, he said. He said he had not heard of D.E.I., referring to diversity, equity and inclusion policies favored by Democrats, until recently.

His values, Mr. Wright said, “have always been conservative.”

Mr. Wright has conducted a traditional campaign for the office, visiting with industry groups and Republican clubs. The state’s “Big Three” Republican leaders — governor, lieutenant governor and House Speaker — all back Mr. Wright re-election, as do the agency’s two other commissioners, both Republicans.

“With Jim Wright at the Railroad Commission, Texas’ energy future is secure,” Mr. Abbott’s campaign spokesman, Eduardo Leal, said.

Incumbents in Texas have had a tough time this year. The state’s longtime agriculture commissioner was ousted in his primary. The governor’s pick for Texas comptroller, serving in the job on an interim basis, lost to a hard right challenger. And Mr. Paxton is locked in a close race to oust Senator John Cornyn in the Republican primary runoff.

The winner of the primary for railroad commissioner will face State Representative Jon Rosenthal, a Houston Democrat and an oil and gas mechanical engineer, in November.