If Liz Cheney’s loss to Harriet Hageman in Wyoming’s primary election on Tuesday seems like a bad dream to many of Ms. Cheney’s Democratic admirers, that’s because it is: For a generation, progressives have imagined the moment when the white working class would finally turn against an insular and privileged Republican establishment. That day has arrived. But it isn’t what Democrats dreamed.Apparently uninterested in everyday governing, the new insurgents who elected Ms. Hageman are consumed with demonstrating that they are authentic conservative Republicans. And in that sense, they are succumbing to the same impulses they associate with their liberal opponents: a shrill hostility to different viewpoints, an obsession with virtue signaling and a willingness to purge their own ranks. The older tradition of Republican politics — the one that cradled Ms. Cheney from girlhood and shaped her in office — is still alive, though embattled, even in Wyoming. Progressives who realize that this privileged Republican establishment was a linchpin of our democracy all along may start rooting for a counterrevolution from above rather than a revolution from below.In the not very distant past, Wyoming’s G.O.P. was focused on governing the state by addressing everyday challenges, like distributing a limited number of liquor licenses and funding its public schools. Politics was “frankly boring,” recalled Tim Stubson, a partisan of the old school.The Cheneys exemplified Wyoming’s establishment: They are quiet and diligent legislators, even a little bland. They are also highly educated and wealthy, splitting their time between Washington and Wyoming’s Teton County, one of the wealthiest counties in the United States.Wyoming politics began to change beneath their feet, slowly at first, as the Tea Party rose to power, and then rapidly during the Trump years, as a new guard waged war with the establishment, making politics less about ordinary governance than about identity.We’ve spent the last year traveling Wyoming, from Cheyenne in the south to Sheridan in the north, from Evanston in the west to Wheatland in the east, talking to local political activists and leaders. This obsession with identity left a mark everywhere, but nowhere more obviously than at the recent Republican state conventions. Just a decade ago, few delegates would have attended party meetings with guns strapped to their hips. Now many do. That wasn’t enough for one delegate at the last convention: He reportedly strutted about with a gun fully cocked. In another departure from old norms, many delegates have taken to wearing their cowboy hats inside the convention center. “That’s not a Wyoming thing,” noted JoAnn True, a patron of the old party. This is mostly because there is no need to wear a cowboy hat indoors — unless your goal is to sport a costume that signals a conservative social identity.Virtue signaling is also on the rise. One convention delegate argued that Wyoming schoolchildren should not be required to say the Pledge of Allegiance, since the word “indivisible” suggests that states can’t secede from the union. Another Republican Party figure was criticized for allegedly failing to adopt an appropriately respectful posture during the pledge.Acting the part of a true Wyoming conservative is a delicate art. It’s not only about signaling that you belong to a rugged, rural working class, but also about highlighting your conservative bona fides, which often means exiling anyone who doesn’t toe the line. Now a conservative cancel culture as unforgiving as its progressive rival is sweeping over the Wyoming G.O.P.Ms. Cheney, of course, is the most prominent victim of that cancel culture: She has been censured twice by the party, and now has been voted out of office. But she is just the tip of an iceberg that mostly lies beneath the media’s radar. Other members of the old type have been censured as well. Their crimes are varied, ranging from supporting Medicaid expansion to founding a nonpartisan PAC to fund female candidates.Websites have emerged that help the new censors identify politically incorrect Republicans. WyoRINO, for example, exposes legislators “who falsely claim to be Republicans” by scrutinizing their voting records for the slightest signs of apostasy. According to the site’s index, nearly a two-thirds majority of Wyoming’s Republican legislators are faking it.Those who are formally censured, though, usually have something else in common: They are from the upper class. In recent years the party has censured a wealthy activist, a state senator with a doctorate and a physician. Joe McGinley, the physician — a prominent party leader of the old style — was censured for reasons that are still a bit mysterious. But as a Stanford-trained doctor, he was a perfect symbol of an inauthentic conservative. Joey Correnti IV, a pistol-packing delegate, mocks his supposed haughtiness, claiming that he introduces himself as “Doctor Joe McGinley.”Plenty of the new insurgents are themselves comfortable members of the professional class pretending to be “one of the people.” Some, like Ms. Hageman, simply seem opportunistic, while others sincerely share cultural affinities with Wyoming’s working class. But to its credit, the new identity politics has also done something rare in this gilded age of American politics: It has elevated genuinely working-class citizens into positions of power. For example, Tom James, elected to the State Senate in 2018, grew up in a foster home and campaigned for office as he delivered pizzas. Meanwhile, Frank Eathorne, the current chairman of the state party, previously worked as a Terminix pest exterminator. As Tim Stubson of the old establishment acknowledged, “It’s a much more blue-collar party.”These candidates are starting to reshape the G.O.P. beyond Wyoming as well. Representative Lauren Boebert of Colorado earned a G.E.D., having left high school after she got pregnant. Meanwhile, in New Jersey, a truck driver won a State Senate seat on a shoestring budget. And in Arizona, Rusty Bowers — who resisted pressure from Donald Trump to overturn his state’s election results — was just badly defeated by David Farnsworth, a small businessman and former crane operator with an A.A. degree.For decades, progressives have hoped that the white working class would turn against the affluent bankers, doctors and oil magnates who control the Republican Party. Well, it did. Class warfare of a kind did finally break out. It’s just not the sort of war progressives imagined, much less hoped for.That’s true partly because progressive longings for class war rested on a falsehood. Influential books like Thomas Frank’s “What’s the Matter With Kansas” insisted that the Republican elite was rapaciously consumed with padding its wealth and exploiting its working-class supporters. Like other myths, that critique contained a kernel of truth. Wyoming’s establishment was too insular at times — and it practiced self-dealing on occasion.But whatever its sins, it was also public spirited. It cared about the general welfare of the state and worked hard on its behalf, laboring away for a pittance in a legislature that begins its sessions in the dead of Wyoming’s punishing winter, when driving is treacherous. The new identitarians infiltrating the State Legislature seem less interested in seeking remedies to real problems than in signaling to their base.Thus, they perform small symbolic acts, like pushing a bill that requires local law enforcement officials to ignore federal law that violates the Second Amendment, or sponsoring a bill that prohibited the teaching of critical race theory in Wyoming public schools. It failed because enough traditional conservatives don’t believe it’s a real problem. Tom Walters, a state representative of the old school, observed, “They speak of it as though it’s there, and yet they know all their teachers and they know their teachers aren’t teaching it.”Addressing these phantoms swallows up time, leaving larger issues neglected. Cathy Connolly, the Democratic minority leader in the State House, told us: “We have one of the highest suicide rates in the nation. We now have the highest workplace fatality rate. We’ve got Covid issues. We’ve got hospitals closing. We’re not looking at these issues because we have these stupid bills,” she said, adding an expletive.The right’s new identity craze wasn’t engineered by Donald Trump. It simply created an opportunity that he exploited. But Mr. Trump has rendered identity politics more dangerous than its progressive rival by wedding it to a cult of personality and a campaign to steal an election. Those changes have only widened the party’s class divide: While a substantial majority of white Republican primary voters without a college degree say they would prefer to vote for him in 2024, those with college degrees generally want someone else, according to a July New York Times/Siena College poll.Ms. Cheney’s fall highlights the cultish character of the right’s evolving politics of identity. During her first two terms, she supported Mr. Trump’s positions 93 percent of the time, according to FiveThirtyEight (almost as often as Kevin McCarthy and more often than Elise Stefanik). Yet Ms. Cheney is not only considered to be a “Republican in Name Only” by many Wyoming Republicans — she is the face of the RINOs. At the state convention, one attendee sported a T-shirt that said “No More RINOs” with Ms. Cheney’s name circled and crossed out. To cross Mr. Trump is to become a fake conservative.Sadly, the G.O.P. establishment was not strong enough to save Ms. Cheney. Happily, though, it isn’t dead, even in Wyoming. In fact, it’s far more entrenched than Ms. Cheney’s defeat might suggest. The old guard still controls the State Legislature and Wyoming’s two most populous counties, both of which pushed back forcefully on efforts to censure Ms. Cheney. And in some places the new insurgents have been outmaneuvered and beaten back. For example, in Campbell County, where support for Mr. Trump surpasses that of most Wyoming counties, the establishment wrestled the party away from the new identitarians.Similar fights are playing out in state parties and legislatures from Colorado to Arizona, Idaho, Illinois and Texas, where the new identitarians are gaining momentum, chipping away at the old guard’s power. But even if they continue to advance, their style of politics may also contain the seeds of its destruction. Any party that elevates symbolism over governing risks stirring mass revolt down the road. Some practitioners of identity politics on the left have already discovered that lesson the hard way. When some members of the San Francisco Board of Education busied themselves renaming schools instead of prioritizing reopening them after lengthy closures during the pandemic, they were recalled. Results matter even in the age of identity politics.Though the outcome of the G.O.P.’s civil war is impossible to determine, one thing is clear: Both sides see the conflict in existential terms. As the traditionalist Dr. McGinley said of Ms. Cheney’s race: “The soul of the Republican Party is at stake.” Ms. Cheney fought valiantly for the party’s soul and was celebrated by traditional Republicans in Wyoming for doing so. They don’t believe her cause is lost — and neither should we.Stephanie Muravchik (@stephaniemurav1) and Jon A. Shields are professors of government at Claremont McKenna College and the authors of “Trump’s Democrats.” They are working on a new book about Liz Cheney’s Wyoming and the future of the American right.The Times is committed to publishing a diversity of letters to the editor. We’d like to hear what you think about this or any of our articles. Here are some tips. And here’s our email: letters@nytimes.com.Follow The New York Times Opinion section on Facebook, Twitter (@NYTopinion) and Instagram. More