Bo French, a far-right activist whose rhetoric alienated Texas business and political leaders, won the Republican runoff for a spot on the state’s influential oil and gas regulatory commission, The Associated Press said Wednesday.

The surprising outcome lifted state Democrats’ hopes for winning the seat in November’s general election.

Mr. French beat Jim Wright, the commission’s chairman, who said Mr. French’s online comments against Muslims and immigrants had nothing to do with the office they sought.

Mr. Wright was backed by the governor, lieutenant governor and the biggest names in the oil and gas industry, including Exxon Mobil and Chevron. But that support could not silence Mr. French’s message, which was amplified by far-right influencers like Steve Bannon, a former close aide to President Trump. The message portrayed Mr. Wright as a secret liberal who would overregulate the oil and gas industry.

Just three people are elected to serve staggered six-year terms on the Texas Railroad Commission, the state body that regulates oil, gas, pipelines and mining. Its niche focus and outdated name, a holdover from when it oversaw rail transport, means elections to the commission are largely ignored outside of the state.

The commission’s job, however, is vital, especially during times of global conflict. Texas produces more than 40 percent of the country’s crude oil.

Mr. French will face Jon Rosenthal, a Houston Democrat and oil and gas engineer, in November. Democrats have not won a statewide election in Texas in more than 30 years.

After a failed run for the Texas House, Mr. French rose in prominence as the chairman of the Republican Party in Tarrant County, one of the state’s largest counties and an influential center of conservative activism. He came under fire last year, when he shared a poll on social media asking who was the “bigger threat” to America, Muslims or Jews.

Dan Patrick, the state’s lieutenant governor and a Trump ally, called on Mr. French to resign his county leadership role over the poll. Instead, Mr. French entered the crowded Republican primary for the statewide regulatory job, coming in a close second to Mr. Wright in March and pushing him into a runoff.

Mr. French said the poll, which he deleted, was misinterpreted; he meant to reflect his view that Islam “is the bigger threat.” The backlash did not quiet Mr. French on social media, where he regularly posted anti-Muslim rhetoric and called for the deportation of nearly one-third of the country.

“It’s time Texans play Cowboys and invaders,” he posted in January. “It’s time we remove foreigners from our soil.”

Mr. Wright tried to avoid being drawn in, instead running a campaign focused on the job’s core issues. Mr. French repeatedly criticized him for voting for Democrats in the past, which Mr. Wright admitted, and for accepting $500,000 from a political action committee funded by the Las Vegas Sands, a casino company.

Mr. French’s campaign was heavily funded by Tim Dunn and Farris Wilks, two West Texas oilmen, who also supported him through a PAC.