Plenty of small media start-ups these days believe they can deliver the final blow to the tottering neoliberal order. But Compact, a self-described “radical American journal” debuting this week, is taking an unusual cross-ideological approach to the task of challenging, as a note from its editors puts it, “the overclass that controls government, culture, and capital.”

“We’re here to start a two-front war on the left and the right,” Matthew Schmitz, one of the magazine’s editors, said in a recent interview with his partners, Sohrab Ahmari and Edwin Aponte.

“I’m not much of an interventionist,” Schmitz hastened to add, “except when it comes to political polemics.”

A joint venture of two religious conservatives and a Marxist populist, Compact reflects the current continuing political realignment, as the resurgence of class-based politics on both sides of the divide has scrambled ideological lines. Its mission: promoting “a strong social-democratic state that defends community — local and national, familial and religious — against a libertine left and a libertarian right.”

Compact is also part of an independent media gold rush, as new, or newly reconfigured, political magazines, podcasts and newsletter platforms have opened up fresh (and sometimes highly lucrative) opportunities outside traditional media.

The idea, Ahmari, a former Op-Ed editor of The New York Post famous for starting flame-throwing feuds with fellow conservatives, wasn’t to “fix” the right or the left, but to publish “really sharp critiques that transcend the categories.”

Aponte, founding editor of the website The Bellows (tagline: “Labor Populism for the Future”) and Compact’s house Marxist, jumped in: “Or treat them as irrelevant?”

Compact, which went live on Tuesday, is certainly an eclectic brew. The first dozen articles — with one to follow daily — include salvos against NATO overreach, “zombie Reaganites” and the “aesthetic castration” of straight male artists.

The masthead of columnists and contributing editors mixes Catholic anti-liberals and dissident Marxist feminists, European radicals and American populists, with prominent figures (Glenn Greenwald, Patrick Deneen) alongside those who cut their teeth on upstart blogs and podcasts.

In an interview, R.R. Reno, editor of the conservative religious journal First Things, who knows both Schmitz and Ahmari well, predicted Compact would “kick up a lot of dust.” But to succeed, he said, “it’s going to have to find that fine line of saying things that are shockingly counter-consensus, but plausible enough they aren’t written off as cranks or irrelevant.”

“Matthew is a very good judge of timing and tone, and when to throw the Molotov cocktail,” Reno added. “Whereas Sohrab’s impulse is always to throw the Molotov cocktail.”

Ahmari, 37, is one of the more flamboyantly pugilistic characters on the right. An Iranian-born onetime Marxist atheist turned neoconservative golden boy turned “post-liberal neo-traditionalist” Catholic, he has drawn attention for his “dazzling flair for individual self-definition as well as a knack for stoking outrage,” as the Daily Beast put it last year. (There’s also his fondness, critics charge, for Viktor Orban’s Hungary.)

The Nebraska-born Schmitz, 36, also a Catholic convert, is more reserved, with a tweedy manner and a more conventional-seeming conservative résumé. After college at Princeton, he worked at the Witherspoon Institute, a socially conservative think tank, before joining First Things.

Today, Schmitz, who is also a columnist for The American Conservative, calls himself “a conservative on social issues, more heterodox on economics, with an instinctive American patriotism and suspicion of our interventionist foreign policy elites.”

He paraphrased Norman Mailer: “You can call me anything you want, just don’t call me a liberal.”

Compact began hatching in December 2020, when Schmitz and Ahmari sat down to discuss a new magazine that would reflect their shared frustrations with the limitations of conservative journalism.

Both had signed “Against the Dead Consensus,” a much-discussed 2019 manifesto in First Things calling for a new conservatism to replace fusionism, the postwar conservative blending of free-market ideology, traditional family values and hawkish foreign policy that had been “blown up” by the election of Donald Trump.

That letter, along with a fire-breathing follow-up by Ahmari calling on conservatives to wage “cultural civil war” against tyrannical liberal individualism (epitomized by Drag Queen Story Hour at public libraries), touched off months of fierce (if hard-to-decipher) debate on the right.

They initially considered starting a traditional conservative magazine, a nonprofit backed by foundations or donors. But they decided to pursue an independent, for-profit path, to be jump-started by investors (whom they declined to name) but eventually supported by subscribers.

Last April, they approached Aponte, a former member of Democratic Socialists of America who started The Bellows in 2020 as an alternative in a left overwhelmed by “liberal identity politics, victim culture, and intersectionality,” as its Kickstarter page put it.

Schmitz said he had been impressed by the site from the beginning, but had really been struck by “The Great Covid Class War,” by Alex Gutentag, a then-unknown California public-school teacher, who argued that lockdowns, vaccine passports and other policies were a smoke screen for “a brutal reorganization of labor.” (Gutentag, now a columnist at Tablet, is a contributing editor for Compact.)

Aponte, 38, who said he grew up “very poor” in Florida, said he was easily sold on the project, with the condition that more than half the articles focused on material concerns, and that he and his co-founders would each have equal editorial input. (They are also equal owners of the site, Schmitz said.)

As for his current politics, Aponte rejected the label “post-left,” which has sometimes been used to describe him and The Bellows (and not always as a compliment). He had sometimes used it “ironically,” he said, to describe his movement “from a left-liberalism to a genuine populism.”

Compact’s website, which features a spiffy design by Pentagram, will be updated daily, with no paywall for the first few weeks. The first offerings run to the highly polemical, repeatedly hitting themes like the bankruptcy of liberalism, the corruption of warmongering foreign policy elites and the need for a moral framework to politics.

In an article called “Against Right Liberalism,” the Harvard legal scholar Adrian Vermeule assails those “zombie Reaganites,” who are “trying desperately to thwart the common good” by pushing the worn-out agenda of “free speech, free markets and free use of drones.”

But the magazine also takes an international view of the current populist revolt. Regular columnists include Malcolm Kyeyune, a Swedish socialist currently affiliated with Oikos, a think tank founded by the former leader of the Sweden Democrats, a right-wing populist-nationalist party.

And while most articles focus on politics and economics, there are also cultural offerings, like that essay on “aesthetic castration” by Adam Lehrer, an artist and critic, and an analysis of the movies “Moonfall” and “Don’t Look Up” by the gadfly Slovenian philosopher Slavoj Zizek (title: “The Stupidity of Nature”).

“It’s a strange mix,” Aponte acknowledged. For some contributors, that’s exactly the appeal.

“I think people are absolutely tired of this division,” said Nina Power, a British philosopher and self-described “open-minded centrist” with roots in Marxist feminism whose book “What Do Men Want?” offers a feminist defense of masculinity.

“Left and right are both features of liberalism,” she said. “We’re more interested in the questions that unite us, whatever our political backgrounds.”

A few days before the launch, Schmitz rattled off a mix of names from the guest list for this week’s launch event at “the odiously named KGB Bar” in the East Village, including a few liberal, or liberal-ish, media types.

He said the magazine might prompt some “breaking ranks.” “I think it’s always a scandal if you hang out with someone you’re not supposed to,” he said.

As for Aponte, when asked how his friends on the left might react to his new comrades, he cocked his head, looking slightly amused.

“What do you think?” he said.