CORTEZ, Colo.—It was the middle of Mike Lavey’s first term as mayor when he jotted down a resignation letter and tucked it away in a leather-bound folder. He said he could no longer stomach the divisions that were tearing apart this rural, southwest Colorado town.

Over the past year, Mr. Lavey had watched as this community of 8,700 became racked by tensions over politics, race and Covid-19. The clash in Cortez mirrored similar conflicts across the country, from other small towns to Washington, D.C.

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CORTEZ, Colo.—It was the middle of Mike Lavey’s first term as mayor when he jotted down a resignation letter and tucked it away in a leather-bound folder. He said he could no longer stomach the divisions that were tearing apart this rural, southwest Colorado town.

Over the past year, Mr. Lavey had watched as this community of 8,700 became racked by tensions over politics, race and Covid-19. The clash in Cortez mirrored similar conflicts across the country, from other small towns to Washington, D.C.

A group named the Montezuma County Patriots led what it called Freedom Rides on Main Street to back law enforcement, former President Donald Trump and an end to pandemic-related restrictions. Meanwhile, a separate, smaller contingent, Walk for Justice and Peace, held signs downtown to protest the murder of George Floyd and to support Black Lives Matter.

Every weekend, trucks festooned with American flags, Trump flags, the occasional Confederate flag and emblems associated with the Three Percenter militia movement rumbled down Main Street past the Justice marchers. Some people in town complained to Mr. Lavey that shoppers and tourists were steering clear of downtown businesses.

Desperate to ease the conflict and worried about extremist elements within the Patriots, the mayor reached out to a group of University of Denver mental health specialists focusing on violence prevention. The goal: to find a way to mediate peace between the two factions.

The Denver team had never worked with an entire community before. Using their experience trying to thwart the spread of extremist ideology and school violence, they came up with a plan for what was, in effect, a communitywide intervention. It would all start by persuading a small group of people from different factions to sit down and talk, with the help of a facilitator. Broader, more ambitious community projects would follow.

But bringing the two sides together is taking a level of trust that has proved increasingly difficult to gain in a year of discord over everything from vaccines to policing to school curriculum.

“It was a great idea, but so many things didn’t pan out,” the mayor said recently. “There’s just no coming together in the country—or Cortez.”

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The trouble began after Mr. Lavey—a retired postman and rare Democrat in a county that voted twice for the Republican Mr. Trump—was elected mayor by his fellow city councilors in April 2020, soon after the Covid-19 pandemic began.

As Colorado Democratic Gov. Jared Polis issued various restrictions on nonessential businesses and places of worship, the Patriots started holding Freedom Ride caravans down Main Street every Saturday in protest.

A few weeks later, following Mr. Floyd’s murder by a Minneapolis policeman, protesters started standing silently on Main Street holding “Black Lives Matter” and “Native Lives Matter” signs. The Patriots would thunder past with signs supporting police and Mr. Trump.

In Cortez, which is about 63% white with sizable Native American and Hispanic populations, both sides were largely white.

“The division we have in our community never happened until Black Lives Matter showed up,” said Tiffany Ghere, who runs a popular Cortez restaurant and helped organize the Freedom Ride caravans.

Dawn Robertson, one of fewer than 100 people in Cortez who are Black or part Black, according to census figures, and an organizer of the Justice marchers, said she was shocked at the vitriol she heard from the Patriots’ caravans.

“It was really nasty. Obscene language. People ‘coal-rolling’ us in their trucks with their middle fingers out,” Ms. Robertson said, describing how some vehicles would blast plumes of smoke. “It was hard to stand out there.”

Ms. Ghere said that some participating in the Patriot caravans flew Three Percenter flags because they represent the colonists’ resistance to tyranny. The Confederate flag, she added, is part of American history. “I’m not racist. I’m not homophobic. I’m not a domestic terrorist,” she said.

At a Jan. 2 rally protesting President Biden’s victory over Mr. Trump in the November election, Mr. Lavey said he observed the Patriots harass the Justice marchers before they confronted him too, calling him a Communist and a traitor.

Ms. Ghere and several others were charged with misdemeanor harassment for following and insulting the Justice group, according to a police report. She pleaded guilty but denied wrongdoing.

Concerned about his own safety, the mayor, a Navy veteran, said he started sleeping with a loaded revolver by his bed.

In late January, he noticed a Denver Post story that mentioned a mental health team at the University of Denver specializing in interventions for people who authorities worry are violence-prone. He called Rachel Nielsen, a clinical psychologist who headed the program, the Colorado Resilience Collaborative.

Dr. Nielsen had counseled a Denver teenage girl who tried to join Islamic State, and she helped schools handle students who expressed violent, extremist beliefs. Although Mr. Lavey’s request for help was outside her usual scope, she said he sounded desperate and agreed to help.

Dr. Nielsen recommended Mr. Lavey organize a forum of six or seven people from disparate corners of Cortez: representatives from the Patriots, minority communities, police and a faith leader.

The discussion should focus on a shared vision for Cortez, not ideologies, she said. If the group got through this step, they should work together on communitywide projects like refurbishing a building or a town festival.

“People are so divided that if we’re just talking about the protesting in town, then they’re going to be pissed off even more,” Dr. Nielsen told the mayor. “What if we talk about the core common denominator for people that love Cortez?”

Dr. Nielsen suggested that someone local and trusted by both sides could facilitate the discussion.

Mr. Lavey asked his predecessor as mayor, Karen Sheek, who heads the League of Women Voters of Colorado, if her group would moderate. She declined. Mr. Lavey turned to his old pastor, David Ramsey, who leads a local nondenominational church. He said he was trying to steer his congregation clear of politics. He also declined.

The mayor thought he hit a breakthrough when a local community college teacher who facilitated a city council retreat expressed interest. But that fell through, too, when he discovered that the teacher had been critical of both the Justice group and Ms. Ghere over their tactics.

The competing rallies downtown continued each weekend.

On Main Street, at the Loungin’ Lizard restaurant, a sign declared masks were required. At the nearby Conservative Grounds coffee shop, where the marquee showed a coffee mug with a Three Percenter emblem, a poem in the style of Dr. Seuss about refusing to wear masks was taped to the window.

Mayor Mike Lavey, a retired postman and rare Democrat in a county that voted twice for Donald Trump, at home in Cortez, Colo.

Dr. Nielsen told Mr. Lavey to try again after the summer, when tensions had cooled.

But tensions didn’t cool. The local Rotary Club declined for the first time to sponsor the annual Ute Mountain Roundup Rodeo parade in June, because its membership worried the Patriots and their caravans would disrupt the event, the group’s president said.

In response, Ms. Ghere helped get the local chamber of commerce to sponsor the parade, saying everyone was welcome. Among the pageantry was a float with a Three Percenter flag.

One woman told the mayor she was so upset by the flag, she skipped the rodeo, Mr. Lavey said.

A few nights after the parade, Ms. Ghere said someone vandalized her car, scrawling a picture of a penis and the word “bitch.” She filed a police report.

The Walk for Justice group ended their marches in June after one year and plan on supporting other local events, like an October rally for abortion rights in Cortez.

The Patriots have continued their rides through downtown Cortez on Saturdays, including a large rally on Sept. 11. Ms. Ghere said the event, advertised as nonpolitical, was intended to support first responders. A smattering of Trump flags were flown.

In recent weeks, the group also turned its attention to school board meetings, where Ms. Ghere and supporters have railed against mask and vaccine mandates and teaching critical race theory in schools. The Montezuma-Cortez school board decided not to require masks in schools and isn’t mandating that teachers get the Covid-19 vaccine. The board also recently passed a resolution opposing critical race theory, which argues that America is historically and structurally skewed toward white people.

Ms. Robertson said she is still open to meeting with the Patriots, but not without a mediator. But she also doesn’t see the deeper chasm in Cortez being bridged. Instead, she said she is focusing on collaborating with local officials she feels comfortable working with on specific issues—like a proposal to send mental health professionals instead of police to respond to mental health calls.

After weighing whether he should submit the resignation letter he had stowed away all summer, Mr. Lavey said he began distancing himself from the town’s divisions and dove back into the business of a small town mayor: hiring a public works director, promoting hot-air balloon rides and attending ribbon cuttings for new businesses. Instead of monitoring the Patriot caravans, he spent summer weekends camping in the mountains with his wife.

He finally decided to ditch the plans for the intervention, even with tensions rising over vaccinations and masks in schools. The resignation letter remains in his folder. For now, the mayor said, coexistence will have to suffice.

“I just want Cortez to go back to how we were before,” Mr. Lavey said.

Members of the Montezuma County Patriots have driven through Cortez on Saturdays for more than a year.

Write to Dan Frosch at dan.frosch@wsj.com