PRESCOTT VALLEY, Ariz. — As Shardé Walter’s family cut back on everything from camping trips to Eggo waffles to balance their inflation-strained budget this summer, she became more and more fed up with the Republicans who have governed Arizona for more than a decade.

“You’ve got those hoity-toity Republicans, and then you’ve got ones like me — just trying to live,” Ms. Walter, 36, said as she waited for former President Donald J. Trump to arrive at a rally on Friday for his slate of candidates in Arizona’s bitterly fought Republican primaries.

“We’re busting our asses off,” she continued, “but we’re broke for no reason.”

The Aug. 2 Republican primary in Arizona has been cast as a party-defining contest between traditional Republicans and Trump loyalists, with the power to reshape a political battleground at the heart of fights over voting rights and fair elections. Several leading Republican candidates in Arizona for governor, secretary of state, attorney general and U.S. Senate have made lies about the “stolen” 2020 election a centerpiece of their campaigns.

But the choice between traditional conservatives and Trump-backed firebrands is also tapping into working-class conservatives’ frustrations with a state economic and political system firmly controlled by Republicans, highlighting the gap between voters who have profited from Arizona’s rising home values and tax cuts tilted toward the wealthy, and those who feel left out and are eager to punish the Republican establishment at the ballot box.

“It’s like ‘The Great Gatsby’ — old versus new,” said Mike Noble, the chief of research with the polling firm OH Predictive Insights, which is based in Phoenix. “It’s a very telling moment for the G.O.P. Are they going the way of MAGA, or the McCain-Goldwater conservative way that gave them dominance over the state?”

National surveys of Republicans show that voters’ views of Mr. Trump and the 2020 election are fracturing along lines of education.

A New York Times/Siena College poll released this month found that 64 percent of Republican primary voters without a college degree believed that Mr. Trump was the legitimate winner of the 2020 election. Forty-four percent of Republican voters with a bachelor’s degree or more said Mr. Trump was the winner.

Mr. Trump was still a clear favorite for Republican voters with a high school degree or less, with 62 percent saying they would vote for him in the 2024 Republican presidential primary if the election were held today. Less than 30 percent of Republican primary voters with college degrees said they would vote for Mr. Trump.

In Arizona, the Republican establishment has coalesced around Karrin Taylor Robson, a wealthy real estate developer pitching herself as a competent leader who has been reliably conservative ever since her days as a staff member in the Reagan White House.

The Trump wing of the party is locked in behind Kari Lake, a Trump-endorsed former news anchor who has stoked an anti-establishment rebellion fueled by falsehoods about the 2020 election and provocations like vowing to bomb smuggling tunnels on the southern border.

Ms. Robson has cut into Ms. Lake’s early lead in the polls, but recent surveys suggest that Ms. Lake is still ahead.

A forthcoming poll of 650 Arizona Republican primary voters by Alloy Analytics found a 10-point lead for Ms. Lake, largely on her strength with working-class voters, though other surveys show a much tighter race. Ms. Lake had a 15-point edge with voters whose families earn less than $50,000 a year. Republicans earning more than $200,000 a year supported Ms. Robson by 14-point margin.

Ms. Robson has lent her campaign $15 million and blanketed local television with ads. She has racked up a long list of endorsements from law-enforcement groups, Arizona’s three living Republican governors and prominent national Republicans, including former Vice President Mike Pence and former Gov. Chris Christie of New Jersey.

Both women are running as anti-abortion, pro-gun, pro-wall conservatives who vow to mobilize law enforcement to address what they call a migrant invasion. Neither misses a chance to excoriate President Biden and Democrats for inflation, crime or culture-war flash points like critical race theory.

Each has tried to claim the mantle of the only true conservative in the race. In a debate, Ms. Lake attacked Ms. Robson for refusing to join other candidates in raising her hand and declaring — falsely — that the 2020 election had been stolen. Ms. Robson tells voters that 2020 was “not fair,” pointing to news media bias and pandemic-driven changes to voting rules. In a recent CNN appearance, she declined to say whether she would have certified the 2020 results, as Mr. Ducey did.

In an interview, Ms. Robson said Ms. Lake’s posture as a conservative “has no basis in truth,” and her campaign attacked Ms. Lake for once supporting former President Barack Obama.

“She’s a really good actress,” Ms. Robson said. “We have real issues we have to deal with, from water to housing to inflation.”

Ms. Lake’s populist homilies and story of a Trump-era political awakening resonate with nontraditional conservatives who say they feel left out of mainstream Republican politics. Ms. Lake’s campaign did not grant an interview.

Moderates say that they simply want a reliable Republican to hold the governor’s seat, and that they are reassured by Ms. Robson’s reams of endorsements and policy plans.

On Friday, the divisions between the two candidates came into sharp focus at competing rallies where Ms. Robson was cheered on by Mr. Pence, and Mr. Trump appeared alongside Ms. Lake.

In Peoria, Ariz., a suburb of Phoenix, the rally for Ms. Robson felt like a supersized Chamber of Commerce luncheon.

Hundreds of voters in Casual Friday polo shirts and summer-weight blouses sat eating barbecue inside a plant that makes military-style tactical gear as Mr. Pence and Gov. Doug Ducey gave speeches endorsing Ms. Robson as a keep-the-faith conservative.

Later that evening at the Trump event, Ms. Lake derided Mr. Ducey as a “weakling” on border security and “do-nothing Ducey.” Mr. Ducey has earned Mr. Trump’s wrath for certifying Mr. Biden’s 10,000-vote victory in Arizona, even as he signed a new voter-identification law opposed by Democrats and has supported fringe right-wing politicians like State Senator Wendy Rogers.

Ms. Robson’s supporters said they, too, felt pinched by rising prices, but, more urgently, they wanted their next governor to be an electable conservative instead of a bomb-throwing heir to Mr. Trump.

“The things she’s worried about, we’re worried about,” said Barb Leonard, 55, who works in software and lives in Scottsdale. “The border, the economy, police.”

Some voters said they did not buy the falsehoods about election fraud that Mr. Trump and Ms. Lake have been peddling for months. Others said they wanted Republicans to stop fixating on the 2020 election and focus instead on border security, school funding and bipartisan laws to cope with Arizona’s worsening drought, water shortages and wildfires.

Political analysts in Arizona said that some voters appeared to be rallying around Ms. Robson as the least divisive general-election choice. Democrats are expected to nominate Secretary of State Katie Hobbs, who defended Arizona’s election system against attacks from Mr. Trump and his allies.

“I don’t want to raise kids in a country that hates each other,” said Derek Weech, 23, a Brigham Young University student and a supporter of Ms. Robson who is working on starting his own business. “Focusing on the last election will not get us to victory.”

So far, Republican primaries this year have been a mixed bag for Trump-endorsed candidates running on election denialism. J.D. Vance, the “Hillbilly Elegy” author, won his primary for U.S. Senate in Ohio. Doug Mastriano won the Republican governor’s primary in Pennsylvania after leading efforts to overturn the 2020 election results there.

But last month in Colorado, Republican voters nominated a businessman who accepted the 2020 election results in a competitive U.S. Senate race. In Georgia, voters delivered a stinging defeat to Mr. Trump by overwhelmingly supporting the incumbent Republican governor and secretary of state who both refused to overturn the 2020 election results there.

In Prescott Valley, the anti-establishment message and an appearance from Mr. Trump was enough to draw thousands of supporters through the doors.

They poured into an arena wearing their defiance and frustration on T-shirts that read, “Trump Won,” “Jihadi Joe” and “Let’s Go Brandon,” the thinly veiled profanity toward Mr. Biden.

As Ms. Lake spoke to the crowd, she received rapturous applause with every dig at Mr. Biden and call to finish the border wall. But one of the biggest cheers came when she mentioned her plan to let high-schoolers focus on learning trades after their sophomore year.

That idea instantly won over Bruce Laughlin, a retired auto technician, and his wife, Cheryl, a dental assistant.

“Neither of us went to college,” Ms. Laughlin said.

“We need carpenters. We need plumbers,” her husband said. “They’ve been totally ignored.”

Janet Olson, 50, said soaring gas, electricity and grocery bills made it feel as if she was not sharing in Arizona’s prosperity. She has just enough left over every month for one indulgence; on Friday, she pumped her last $9.95 into her truck and drove from outside Phoenix to the mountains to see Ms. Lake and Mr. Trump.

“Every month it’s harder,” Ms. Olson said.

She said she felt alienated from Arizona’s mainline Republican Party, but at home with the people waiting with her in concessions lines to buy bottled water $4.50 and nachos for $5.

“We don’t want bow ties and caviar,” Ms. Olson said. “We want corn dogs and funnel cakes. And Kari Lake.”

Will Davis contributed reporting.