Ask any Republican and they'll say that they are losing the culture war in practically every battle.
Are they right?

According to Republicans it's liberals who are on the offensive, and the things they are pushing are unpopular and will alienate working class America.

Virginia’s Loudoun County is a good example. Situated near D.C., the upwardly mobile suburban area has become the epicenter of school board overreach. Parents have opposed the teaching of critical race theory and controversial books.
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A few days later, one of these dads revealed that his ninth-grader had been sexually assaulted in a school bathroom and the crime covered up by the school board. When he attended a meeting to complain, the board had him arrested.

The attacker was a boy in a girl’s bathroom, and the board feared it would stall their priority of allowing students to use the bathroom of their choice. This culture war issue was more important to Loudoun County than academics or the physical safety of their students.

For Republicans, what is happening is nothing short than a collapse of civilization, and liberals are agents of Satan. Thus they are treasonous and evil.

In looking at the long history of conservative politics, from the defeat of Robert Taft in 1952, to the nomination of Barry Goldwater, to the takeover of the Republican Party in 1994, I think it is fair to say that conservatives have learned to succeed in politics. That is, we got our people elected.

But that did not result in the adoption of our agenda. The reason, I think, is that politics itself has failed. And politics has failed because of the collapse of the culture. The culture we are living in becomes an ever-wider sewer. In truth, I think we are caught up in a cultural collapse of historic proportions, a collapse so great that it simply overwhelms politics.
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whenever an elite liberal commentator said something fringy, one could always console himself by saying (or at least thinking): "I hope you push that idea, because you'll keep losing elections in real America."

Conservatives absolutely despise the elites. Leftists hate the elites too.
However, the elites that conservatives hate are NOT the ruling elites. They are the "cultural elites" of the "radical left". Which by their definition are mostly college professors and Hollywood movie stars, rather than the billionaires which actually run the country.
The "radical left" has gone crazy and is alienating even progressives.

The social justice obsessed, ultra-progressive, increasingly illiberal Left is even alienating liberal celebrities. Once feted as a progressive darling, Tesla CEO Elon Musk tweeted in May that he can no longer support the Democrats. “In the past I voted Democrat, because they were (mostly) the kindness party,” he wrote. “But they have become the party of division & hate, so I can no longer support them and will vote Republican.”

So conservatives know how to win elections, but liberals know how to win the culture war. In fact, liberals are so successful at winning the culture war that they are alienating most Americans.

Which doesn't make any sense at all. You can't be winning a culture war if most people hate you and your culture and it is causing you to lose elections.
This narrative is based on a deliberate fiction.

Let's start with critical race theory.

Virginia’s new governor, Glenn Youngkin, kicked off his term with a political magic trick. In the first of nine executive orders issued on Jan. 15, the day he took office,1 he banned the teaching of “inherently divisive concepts, including critical race theory” in K-12 public schools. It was a smart way to show his base he’s already jumping on issues they care about. Education policy, particularly the alleged role critical race theory plays in public school curricula, was a centerpiece of Youngkin’s campaign. But the impact of this executive order is less straightforward than it seems, because critical race theory isn’t actually taught in Virginia public schools.

Critical Race Theory is only taught in college and it's an elective course. The entire CRT issue is a strawman creation. Republicans have created a political firestorm out of nothing, and then blamed the "far left" for waging a culture war against conservatives, when nothing could be further from the truth.

According to a Reuters poll 31 percent of Republicans said they believed that critical race theory “says that discriminating against white people is the only way to achieve equality.” Moreover, 22 percent said they believed that critical race theory “says that white people are inherently evil or bad.” In fact, critical race theory says neither of these things.
Of course, not all of the Republican culture war issues are entirely fabricated. Sometimes they take a real event and then turn it into something completely else. A great example is that Loundun County high school rape mentioned above.

Smith revealed why he’d been so distraught. In an interview with The Daily Wire, a website co-founded by the conservative wunderkind Ben Shapiro, Smith said that his ninth-grade daughter had been sexually assaulted in a school bathroom by a boy wearing a skirt. Smith was opposed to a proposed policy allowing trans kids to use bathrooms aligned with their gender identities, believing it made girls like his daughter vulnerable.

“The point is kids are using it as an advantage to get into the bathrooms,” he told the reporter, Luke Rosiak...
After Rosiak’s article came out, Smith became a symbol of a different kind: a blue-collar martyr to wokeness. Appearing on Tucker Carlson’s Fox News show, Rosiak said, “This story is one of the most disturbing I’ve ever worked on. It raises the possibility that the Loudoun County public schools covered up the rape of a 14-year-old girl at the hands of a boy wearing a skirt in order to pass a school policy that Democrats were adamant about passing.”

Conservatives have long argued that letting trans girls and women into women’s bathrooms would lead to sexual predation, and now that seemed to have happened. They’ve argued that wokeness is a form of tyranny, and in Smith they had a man who seemed to have been tyrannized because his family’s lived experience posed a threat to trans ideology.
If they had it all wrong, it’s almost hard to blame them — the narrative was too irresistible.

The only things true about this was that the girl was raped, and that the boy was wearing a dress. Everything else was a lie. The boy wasn't a trans, and was the girl's boyfriend. It was the girl's idea to meet in that bathroom where they had had sex before. Also the school didn't have a bathroom policy for trans students at the time.

This kind of tactic is increasingly familiar in politics today. Republican politicians, in particular, build entire campaigns around false or misleading information, then implement policies that respond to those falsehoods, cementing them further in our political landscape.

Conservatives scream that they are the victims of the "radical left's" culture war, and most Republican voters actually believe it. In reality, conservatives created the issue out of whole cloth, and then used it to launch a political agenda which has allowed conservatives to take over school boards all over the country.
At least nine state legislatures have tried to ban critical race theory from being taught in public high schools.

Then there are issues that are not cultural issues, but have become part of the culture war battlefield anyway, such as the source of the COVID virus.
Conservatives have embraced the lab leak theory, which may indeed to true. Liberals have responded by calling it a conspiracy theory, which may also be true.
Interestingly liberals have decided that the lab leak theory was racist, despite the fact that the alternative (supposedly not racist) theory was that the virus emerged in a nearby market where the local Chinese ate, what Americans normally consider, strange food.
How this theory is any less racist is something I do not understand.
Either way, if the source is finally proven it is unlikely that both sides will ever accept it.

Liberals have plenty of their own culture war issues. Namely anything regarding race, gender, and sexual preference, with race reductionism leading the way.
However, it wasn't until recently that liberals decided to simply invent issue out of nothing, such as Russiagate.