In some of Mr. Masters’s earliest television and digital ads, he claimed without evidence that Mr. Trump had won the 2020 election and called for a militarization of the United States’ border with Mexico. His immigration ads had a video game-like quality, featuring ominous music, stark desert backdrops and faceless masses of migrants.

On his website, as in speeches and podcasts, he echoed a sanitized version of the racist “great replacement” conspiracy theory, claiming that Democrats were trying to bring more immigrants into the country to change its demographics and give the party an edge.

But since the Aug. 3 primary, Mr. Masters has tried to soften his tone, seeking to focus his bid on inflation, crime and illegal immigration. Before the primary, three of the four television ads that were paid for by his campaign captured him alone in the desert. Since then, two of his campaign’s three ads have featured his wife and children.

His website has also undergone a cleanup: A line about Democrats purportedly importing immigrant voters has been removed, and he was one of several Republicans to take down false claims of a rigged 2020 election. His site deleted mentions of his support for some of the most stringent abortion restrictions, including “a federal personhood law (ideally a Constitutional amendment) that recognizes that unborn babies are human beings that may not be killed.”

A person close to Mr. Masters told CNN last month that the candidate wanted his website to be seen as a “living document,” and he told the radio station KTAR News this month that any changes to it reflected “a new way that we’re talking about something, but it’s not a backtrack or anything like that.”

Mr. Masters, who often appears with Ms. Lake, has not completely abandoned his combative instincts. He recently drew criticism for describing Vice President Kamala Harris as a beneficiary of an “affirmative action regime.” This month, he declined to commit to accepting this year’s election results.

Mr. Masters’s supporters are unfazed by his attempts at moderation. They still see him as a potential bulwark against President Biden and what they describe as “radical” Democrats who want to regulate guns, open the border and take control away from parents in schools.