For the past three and a half years, Republicans have struggled to explain a great conundrum. If they are the party of authentic America with a mystical connection to the will of the people, then how, exactly, did Barack Obama get elected president?

Some Republicans have come up with an answer that allows them to avoid facing the unpleasant reality of their own party’s failures: Obama must be a great deceiver. He won the White House by subterfuge.

Claims that Obama concealed nonnative birth or faith in Islam failed to gain mainstream traction, but conservatives like Sean Hannity were more successful in labeling Obama as covertly “anti-American” based on his association with the incendiary pastor the Rev. Jeremiah Wright. By this logic, Obama was a paragon of Christian piety. He “savored” every word on Sunday mornings and would surely govern by these traitorous principles: his beliefs were dangerous because, well, he really believed them.

Now his critics have reversed course: they say Obama is a sham Christian. He thinks religion is not heartfelt belief that demands full expression, but only a matter of showing up at church. He is not the first president to stand so accused: in the election of 1800, one clergyman charged Thomas Jefferson with “disbelief of the Holy Scriptures,” and Abraham Lincoln battled the suggestion that he was a “scoffer of Christianity.”

But Obama’s opponents have a new twist on this old allegation. They find evidence for his unbelief not by exposing his biblical illiteracy or shoddy church attendance, but in his failure to support “religious freedom.”

Religious freedom is as American as apple pie, isn’t it? How could anyone oppose it? Because — this line of reasoning goes — Obama is not who he says he is. He claims to be a true Christian and a true American, but his actions prove otherwise.

The charge that the president is a faker on religious freedom is the most recent iteration of the ongoing attack on his legitimacy: it is the new “birther” movement. It’s also a decades-old rhetorical tool of the culture wars intended to depict the entire left as frauds who supposedly stand for a tolerant open society, but who are in fact disciples of a secular pseudo-religion intent on quashing Christian influence in America.

The Rev. Franklin Graham, who has always been more provocative than his prudent father Billy, told MSNBC last week that the president lacks sufficient outrage over the plight of persecuted Christians. “Islam has gotten a free pass under Obama,” Graham said, adding that the Muslim world sees Obama as “a son of Islam” who will not challenge religious oppression. “The Muslims of the world — he seems to be more concerned about them than the Christians that are being murdered in the Muslim countries – that’s what bothers me.” (Graham offered a half-apology on Tuesday, saying he regretted any comments that “cast any doubt on the personal faith of our president.”)

During the recent outcry over the Obama administration’s new rule requiring religious employers to cover birth control in their insurance plans, Newt Gingrich and Mitt Romney blasted the president too: here was proof of Obama’s aim to oppress religious expression and trample constitutional rights.

Last week, at a rally at a Christian college in Michigan, Rick Santorum called the president “particularly weak” on religious freedom. He insisted that “freedom of religion” is much more than “freedom of worship” confined within a church’s four walls, which even “tyrants” support. “When you have the president of the United States referring to freedom of religion and you have the secretary of state referring to the freedom of religion, not as the freedom of religion but the freedom of worship, you should get very, very nervous,” he warned.

When conservatives cry “freedom of religion” and insist they mean something more than “freedom of worship,” this is what they mean: religious freedom is not just the freedom to gather in a room and pray one morning a week. It is the freedom to impose one’s own religious values on others. Free expression of religion entails the right to reason from religious principles in the public square and — with sufficient electoral support — to enshrine those principles in law and social institutions. If Obama does not support this view, they argue, then he is hardly a true American.

Over the course of American history, “religious freedom” has been a shape-shifter invoked just as often in the name of prejudice (in 19th-century Protestant campaigns against Catholic schools; in fundamentalist colleges’ racial discrimination a hundred years later) as on behalf of liberty. It is a code phrase alternately benign and sinister, much like that other clever cloak for bigotry, “states’ rights.” In the context of the 2012 race, the charge that Obama subverts religious freedom is a code meant to label the president as an impostor, a blasphemer of the American gospel who adheres to another religion entirely.

Santorum has hit this theme the hardest, warning that conservative Christians must not be fooled by the president’s efforts to play the neutral statesman who treats all believers equally. On the contrary, he obeys a false religion with nonnegotiable assumptions of its own. Santorum described Obama’s environmentalism as a “phony theology” and a “worldview.”

This is an attempt to paint as irrationally ideological a president who has proven himself to be not very ideological at all (much to the frustration of his supporters on the left). It is a culture warrior’s maneuver to cast American politics as a Manichean battleground between two worldviews — red-blooded Christian America pitted against the secularist stranger — worldviews so captive to their own logic that they cannot possibly compromise on anything.

This obsession with “worldviews” has been a favorite tactic of the Christian right. In the 1970s, Francis Schaeffer and other activists taught evangelicals to organize against the “secular humanist worldview” that was denaturing America’s Christian values in an acid bath of “humanist religion,” “an exclusivist, closed system which shuts out all contending viewpoints” (that’s the “phony theology” that Santorum was talking about).

Schaeffer’s admirers often note that he defends religious freedom in his 1981 book, “A Christian Manifesto.” But after Schaeffer called for “general religious freedom” for all faiths, he went on to lament the left’s manipulation of the First Amendment to encourage a “new concept of pluralism” in which “there is no right or wrong; it is just a matter of your personal preference.”

To recover America’s biblical foundation, Christians had to “do battle on the entire front:” not just in church, but in the courts, classrooms, outside abortion clinics and everywhere else, Schaeffer wrote. The emerging Christian right asserted that this was the true meaning of “religious freedom” in America: freedom to institutionalize Christian dogma in American society and law. Freedom of religion — a phrase that sounds at first blush like a bipartisan nod to our common political heritage — is a weapon of culture war.

Slogans like this have political power. Voters on both the right and the left have little sympathy for politicians who reason through problems and recognize ambiguity (conservatives won’t forgive Romney for his honest struggles with the abortion issue, and Obama faces liberal wrath for his nuanced approach to economic recovery). Wonkish debates are boring and complicated, and not very good for separating the sheep from the goats. What matters are your “presuppositions,” your “worldview.”

Conservatives’ accusations that Obama disrespects religious freedom have little to do with the White House’s actual policy: his administration has a strong track record in supporting faith-based organizations and ensuring that prisoners have access to religious literature, for example. They have everything to do with resurrecting old challenges to the president’s legitimacy and framing the 2012 campaign as a battle between honest Christian Americans and atheist subversives. “Enemy of religious freedom” is shorthand for a deceiver who is not one of us: in Gingrich’s words, one who “played a wonderful con, as a result of which he is now president.”

Molly Worthen teaches religious history at the University of Toronto.