Turns out same-sex marriage isn’t just bringing couples together.

The liberal Constitutional Accountability Center and the libertarian Cato Institute don’t agree on much. The two organizations have disagreed on legal battles over the Affordable Care Act, environmental regulations, labor laws, voting rights, and campaign finance.

“Pick the case, we’re usually on the opposite side,” said Ilya Shapiro, a senior fellow with the Cato Institute. “But every few years there’s something we agree on.”

Where the two organizations stand on common ground: Same-sex marriage bans are unconstitutional.

Last year, the groups teamed up to file legal briefs in the challenges to California’s ban on same-sex marriage and the Defense of Marriage Act, which barred federal recognition of same-sex marriages performed in states where such couples are allowed to marry. Since gay and lesbian rights supporters prevailed at the Supreme Court last summer, federal courts across the country have been striking down same-sex marriage bans based on the legal reasoning in those rulings. The liberal Constitutional Accountability Center and the libertarian Cato Institute are joining forces again, seeking to urge federal courts to recognize a constitutional right to same-sex marriage. They’ve filed a brief together in the Utah and Oklahoma same-sex marriage cases, and plan to do so in other pending same-sex marriage cases.

Both groups are in complete agreement about bans on same-sex marriage, which they write violate the 14th Amendment’s “guarantee of the “equal protection of the laws” is sweeping and universal.” This isn’t the first left-right collaboration on same-sex marriage, of course. Democrat David Boies and Republican Ted Olson, who were on opposite sides of Bush v. Gore, famously worked together in their successful challenge to California’s Proposition 8, and are now working to strike down same-sex marriage bans in the states.

Though Cato and the CAC often come to very different conclusions, the groups actually share something of a similar philosophy regarding constitutional interpretation. Originalism, the theory of constitutional interpretation that places a priority on the “original meaning” of the Constitution, is usually associated with conservatives and libertarians. But the Constitutional Accountability Center adheres to what is sometimes called “liberal originalism“ or “new textualism,” which takes a comparable approach, but holds that exploring “original meaning” matches up with liberal beliefs more often than expected.

“Too often progressives cede the Constitution to conservatives, in the courts and in the public square, but we do that at our peril – especially since the Constitution so often points to progressive outcomes,” said Doug Kendall, head of the Constitutional Accountability Center. Kendall said the two groups’ “collaboration on marriage equality cases should be a wake-up call to liberals about the power and progressive promise of the Constitution’s text and history.”

The liberaltarian romance between the two groups began in 2009 with a gun rights case, in which Cato and the CAC unexpectedly ended up on the same side. Many liberal and conservative legal scholars view an old group of post-Civil War cases known as the “Slaughterhouse cases,” as a regrettable episode in American legal history because the cases substantially weakened civil rights granted by the 14th Amendment. Cato and CAC both saw the 2009 gun rights case as an opportunity to reverse that decision. Though the Supreme Court didn’t go as far as they wanted, the two groups realized they might have some common interests.

Shapiro jokes that “every five years we’re on the same side. First it was guns, now sex and the next one will be drugs.”