The Obama administration’s new mandate that religious organizations pay for their workers’ birth control has become a bludgeon for Republican culture warriors, as social issues have surged to the forefront in the presidential campaign.

Conservatives who believe religious freedom always trumps gender equity in the public arena are outraged. But so too are Roman Catholic and evangelical moderates who have stuck with President Barack Obama, an abortion rights supporter, because of his 2008 pledge to reduce the abortion rate and find common ground among religious and secular Americans. These backers say the administration could have easily avoided the controversy by including broader religious exemptions already in place at some federal agencies.

After two weeks of unrelenting condemnation led by the nation’s Catholic bishops, the White House has responded by hinting at some compromise in how the requirement is enforced. Administration officials insist any accommodation for religious groups will leave in place contraceptive coverage, although they haven’t said how. But even the suggestion of a revision, no matter how limited, has infuriated Democrats the president hoped to please with the regulation. As the debate rages, women’s groups, liberal religious leaders and health advocates are rallying in favor of the broadest contraceptive coverage that would include Catholic employers.

“We believe that women and men have the right to decide whether or not to apply the principles of their faith to family-planning decisions, and to do so they must have access to services,” read a statement Wednesday from liberal religious leaders representing Reform and Conservative Jews, Methodist and Episcopal groups, among others. “The administration was correct in requiring institutions that do not have purely sectarian goals to offer comprehensive preventive health care.”

The conflict is erupting as GOP candidates compete for the title of the true conservative in the presidential race. The contraception debate is tailor-made for the fight.

Newt Gingrich, a Catholic, told Ohio Republicans that the policy was “the Obama administration’s attack on the Catholic Church.” Rick Santorum, also Catholic, said the administration was trying to “use their power to force people” to violate their beliefs.

Mitt Romney, who mostly avoids religious specifics to deflect attention from his Mormonism, has also taken up the issue. In Colorado, Romney called the policy an “assault on religion,” and “a real blow ... to our friends in the Catholic faith.”

White House spokesman Jay Carney called it “ironic that Mitt Romney is criticizing the president” for a policy that Carney described as identical to the one Romney followed as Massachusetts governor.

House Speaker John Boehner said in a speech from the floor Wednesday that the Health and Human Services Department mandate was “an unambiguous attack on religious freedom.” If the president doesn’t reverse the new policy, Congress will, Boehner said.

The debate is stealing attention from where Obama wants it, on the improving economy, and could alienate moderate voters.

For decades, Christian right activists have been fighting against what they call a war on religion, ever since the Supreme Court ended sectarian prayer in schools and legalized abortion. As acceptance of gay marriage grows, religious conservatives increasingly view themselves as a besieged minority in an ever more permissive society. Catholic leaders have taken to calling the church the true counterculture.

However, the contraceptive mandate has infuriated many Catholics regardless of political ideology because it could potentially damage what they consider the pride of their church: the multibillion-dollar Catholic-run network of hospitals, schools, colleges, homeless shelters and food pantries that mostly employ and serve members of other faiths.

“I don’t think this is the president’s best judgment,” said Douglas Kmiec, a prominent conservative legal scholar and Catholic who has been excoriated by bishops and conservative activists for backing Obama, starting four years ago. “I’ve got a great deal of concern that he has caused for himself an enormous problem with my fellow Catholics that he didn’t need and that will indeed place his re-election in jeopardy.”