The Washington Post's Sean Sullivan talks about how voters in Wyoming reacted to the feud over same-sex marriage between Republican primary candidate Liz Cheney and her sister. (The Washington Post)

Along with the autumn snow flurries, there is a certain touchiness in the Wyoming air among the state’s Republican establishment.

“It’s bruising people,” former senator Alan K. Simpson says of the topic of pretty much everyone’s conversations these days. “When you get a call from Dick or Lynne, and you love them, you don’t want to say no. It’s got Wyoming in a turmoil.”

Dick and Lynne, of course, are the Cheneys, the former vice president and his wife, who are political royalty in Wyoming. And the “it” in question is their daughter Liz’s audacious Republican primary challenge of incumbent Sen. Mike Enzi — which took a painful turn in recent days when Liz’s lesbian sibling, Mary, ramped up her public criticism of her older sister’s opposition to same-sex marriage.

The scant polling thus far indicates that Cheney is running far behind Enzi. But the primary is still nearly nine months away; in the meantime, even social situations in Wyoming are starting to get tricky.

That is especially true for those who are trying to maintain their impartiality and their good relations with both sides.

For instance, after Gov. Matt Mead (R) named the former vice president to his Wyoming team in the annual One Shot Antelope hunting competition in Lander, he balanced that move by partnering with Enzi in Torrington’s 2 Shot Goose Hunt.

Politics isn’t a blood sport in Wyoming. The bare-knuckle political brawling that is the norm in Washington is unfamiliar in this sparsely populated state that takes pride in its cordiality and puts a premium on retail politicking.

But Cheney’s entrance into the race has upended that dynamic, fraying long-standing relationships and in this case, even family ties.

“To see old bonds being ripped,” lamented former governor Mike Sullivan (D) at a business conference here, is “something you hate to see happen.” Sullivan described Wyoming as a “big city with unusually long streets.”

Enzi and Dick Cheney were never seen as political foes. But these days, that could hardly be less clear, with the former vice president lobbing criticism at his daughter’s opponent. That presents Wyoming voters with an unfamiliar rivalry.

Wyomingites are also left to ponder what to make of the Cheneys’ family dust-up, which escalated last week. After a national television interview in which Liz Cheney reaffirmed her opposition to same-sex marriage, Mary Cheney and her wife, Heather Poe, took to Facebook to criticize her stance. In August, Mary Cheney had offered a similar rebuke.

It is all the more perplexing given that gay marriage is not exactly at the forefront of concerns in a state whose motto is “Equal Rights” and whose conservatism generally runs more toward the live-and-let-live variety.

“There’s a joke out here that none of us use turn signals, because it’s nobody’s damn business where we’re going,” said Joe Milczewski, a veteran GOP strategist who managed Sen. John Barrasso’s (R) 2008 campaign and who is staying studiously neutral in the Senate race.

At a minimum, the Cheneys’ internal spat is a distraction for the struggling challenger. More worrisome, the question of whether her private stance on same-sex marriage matches her public one could undermine Liz Cheney in her biggest challenge, which is to convince voters that she is not the carpetbagging opportunist that her critics make her out to be.

“Authenticity has always been the biggest attribute you can have in Wyoming,” Milczewski said. “If you don’t come across as authentic, these ranchers in Niobrara County and Converse County, they’ll smell it a million miles away.”

Liz Cheney, who traces her Wyoming roots back four generations on her mom’s side and three on her dad’s, spent most of her own life in the faraway environs of suburban Washington, where the family moved when she was in high school.

Her relocation to the state in 2012 coincided with speculation that Enzi was thinking about forgoing a run for a fourth term. Any doubt as to her intentions — or the urgency of her ambition — disappeared in July.

Without waiting for Enzi to formally declare his decision, she posted a six-minute YouTube video saying she was in the race; the senator quickly followed with his own announcement, adding balefully of his new opponent: “I thought we were friends.”

Liz Cheney, 47, has accused the easygoing Enzi of being insufficiently conservative — a charge that Wyoming GOP leaders say is laughable. Enzi was more conservative than all but seven of his Senate colleagues, according to National Journal’s 2012 vote ratings, and he has the backing of tea party icon Sen. Rand Paul (R-Ky.).

Liz Cheney also presents herself as part of “a new generation of leaders,” which some might read as another way of saying that the 69-year-old Enzi is old. Cheney denies she means any such thing.

Although Liz Cheney has an identity in her own right as a former State Department official, a foreign policy hawk and a pugnacious television commentator, her chief political asset in Wyoming is the Cheney brand.

Her last name gives her an entree with undecided voters like Joe Paulsen, 41, of Cheyenne, but it won’t close the deal.

“I like the Cheneys a lot,” he said. “But it’s fairly new to me, her being in the race.”

Others remain skeptical of Cheney because of the years she spent away from Wyoming.

“I don’t think Liz Cheney’s got a chance because she has not been in the state that long,” said Rich Moore, 66, also of Cheyenne.

Along with her husband and children, Liz Cheney has settled into a home near Jackson Hole. Neighbors described the family as low-profile residents.

“We don’t really see them very often,” said Nancy Pettus, who lives next door. “I don’t know whether that’s totally because they’re not around much or we just don’t cross paths.”

Andy King, whose house is nearby, said he sees Liz Cheney “periodically” around the neighborhood. “She’s always been nice; she’s very sharp,” he said. The two have yet to broach politics in their encounters.

A well-known part of the Cheneys’ family image of thrumming functionality is the support and protectiveness they have shown toward Mary and her wife, who are the parents of two daughters.

The former vice president, for instance, is publicly in favor of same-sex marriage. However, after Poe suggested in a Facebook post that Liz Cheney was being hypocritical — supporting her sister’s marriage in private while advocating against such unions for others in public — Dick and Lynne issued a statement saying their elder daughter “has always believed in the traditional definition of marriage.”

“She has also always treated her sister and her sister’s family with love and respect, exactly as she should have done,” the Cheneys said. “Compassion is called for, even when there is disagreement about such a fundamental matter, and Liz’s many kindnesses shouldn’t be used to distort her position.”

Primary challenges are inherently uncomfortable experiences for political parties, but they are particularly so when they test loyalties in a state such as Wyoming.

“Politics is personal,” said Simpson, who is supporting Enzi. “There’s only 580,000 of us running around in 98,000 square miles. We know who we are.”

Liz Cheney and Enzi declined to be interviewed for this article, but spokeswomen for the candidates weighed in.

Liz Cheney’s team professes to be satisfied with the kind of race she is running thus far.

“Liz is honored to be in the race and grateful for the outpouring of support she is receiving all over the state,” said communications director Brittany Wells. “She is running a grass-roots campaign focused on the voters of Wyoming and dedicated to winning this race one vote at a time.”

Kristin Walker, a spokeswoman for Enzi, said, “Every race for the Senate he’s run has been won county by county, town by town and block by block. 2014 will be no different.”

But there is a recognition here that this is not just another race and Cheney is not just another opponent. With that in mind, Enzi and his allies are gearing up. A super PAC has formed to support the senator. And Cheney’s fast fundraising start — she outraised the senator from July through September — has forced Enzi to kick his own money machine into gear.

For Wyomingites, it promises to be a long, uncomfortable primary season.

“I hope it doesn’t get more nasty,” said state Sen. John Schiffer (R), who is backing Enzi.

So far, that is looking like wishful thinking.

Sullivan reported from Wyoming and Tumulty reported from Washington. Alice Crites contributed to this report.