A tiny group of voters could deliver one of the most significant results in local US elections on Tuesday when ballots are counted in a remote town run by members of a polygamist sect under the control of a so-called prophet from a prison cell.

For the first time in its troubled history, Hildale, a speck in the wilderness on the Utah-Arizona border, has candidates running for mayor and town council seats who are not associated with the local fundamentalist religious sect, currently run by convicted child rapist Warren Jeffs.

If mayoral candidate Donia Jessop and the three “outsiders” competing for council seats win their races against incumbents on Tuesday, non-sect members will effectively win control of the town.

“If we win we would take the majority of the council and that’s a big deal. Then we could start the process for the whole town changing,” Jessop told the Guardian.

Increasing numbers of people who previously fled the sect or were never part of it have been moving into Hildale. And greater numbers of Jeffs’ followers, who call themselves the Fundamentalist Latter-Day Saints (FLDS), have been leaving amid predictions that the sect is crumbling.

Hildale’s population is just under 3,000 and has only 365 registered voters, who will vote by mail. The council and police force were all chosen by church leaders, until increasing intervention by the conventional authorities in recent years, and now outsiders are running for office.

“There’s been a lot of sadness in the town. I hope more and more will come out from under the oppression of the FLDS,” Jessop said.

Traditionally, the FLDS has banned its followers from access to the internet, TV and outside reading material, though younger members have recently been lured away from the sect by sneaking on to forbidden social media sites. Jessop wants to install internet services for the whole town.

Jared Nicol, who was involved with the FLDS and is a mainstream Mormon, moved to Hildale two years ago and is running for city council. He believes the population has tipped in the last year to become majority non-FLDS.

“We are in a prime position for tourism and I want to try to push that. It’s exciting,” said Nicol.

Hildale sits amid spectacular red sandstone cliffs a few miles from the popular Zion national park, but has traditionally been hostile to visitors.

It was settled in the early 20th century by the FLDS, who disagreed with the mainstream Mormon church outlawing polygamy as a central tenet.

Despite polygamy being illegal, proponents in Utah largely skirt the law by registering just one marriage in each family with the authorities. The men then takes other women as unofficial “spiritual” wives.

Warren Jeffs had dozens of wives, and decreed child marriage acceptable within the FLDS. He has been serving a life sentence since 2011 on charges relating to raping girls aged 12 and 14, whom he had forced to become his spiritual wives. But he still runs the FLDS from behind bars, communicating via letters to subordinates in the church hierarchy.

“The control of Warren Jeffs within the FLDS is still 100% and you see his followers constantly listening to his teachings on their iPods,” said Jessop.

In a twist perhaps only the state of Utah could deliver in modern America, Jessop lives unofficially but openly as a polygamist. At least one of the three other non-fundamentalist candidates tolerates polygamy, while rejecting the strict theocracy imposed by the FLDS, which dictates that the word of Jeffs is divine law. Members must wear prairie dresses and pioneer-era hairstyles.

“I left five years ago. The leaders said my nine-year-old daughter could stay in the church but the rest of us were not worthy,” she said.

She and her husband were ordered to repent by living separately and shunning each other, and would be deprived of seeing some of their 10 children. So she left and tossed the prairie dress. But three years ago her husband took a second, unregistered, “wife”.

“I call her my soul sister. It’s not a religious thing, I’m supportive of any lifestyle as long as it’s adults and no one is getting hurt,” she said.

Jared Nicol said: “We have plenty of neighbors and friends who are part of plural families.” His son has a friend who lives with his father and “three mothers”, he said.

He believes he can be “a bridge” in Hildale between sect members and ex-members, whom the FLDS calls apostates and excommunicates even from their own family members.