Rick Santorum may have extreme views, but at least he describes them colorfully. The man who once likened homosexuality to “man on dog” sex caused a stir again Sunday by saying on ABC News’ This Week that John F. Kennedy’s 1960 speech about religious freedom made him want to vomit. Deploring JFK’s assertion that “the separation of church and state is absolute,” Santorum explained: “You bet that makes you throw up. What kind of country do we live [in] that says only people of non-faith can come into the public square and make their case?”

Santorum can’t be dismissed as a fringe figure in today’s Republican Party, and not just because he’s running even with Mitt Romney in the primaries. Romney, too, has rejected the principles of Kennedy’s speech. Four years ago, facing anti-Mormon prejudice, Romney was urged to issue a Kennedyesque statement on church and state. And although that speech contained some promising lines, like his insistence that “no authorities of my church, or of any other church for that matter, will ever exert influence on presidential decisions,” Romney’s fear of alienating fundamentalist voters eventually led him into incoherence. The separation of church and state had gone too far, he alleged: “Freedom requires religion just as religion requires freedom.” It makes no sense to say that a candidate’s religion doesn’t matter and then to insist that your piety recommends you as a candidate.

Both Republican front-runners, then, have missed the importance of Kennedy’s landmark speech. Contrary to Santorum’s confused reading, Kennedy never said that “only people of non-faith” (whatever that may be) can participate in public or political life—a statement that would have been absurd given his own convictions. Unlike Romney, Kennedy never felt any need to brandish his churchly credentials as proof of his morality, because, as he suggested in the speech, he understood that in a democracy, policy positions have to be secular in nature. His remarks are worth revisiting.

Questions about whether America would ever elect a Catholic were first discussed seriously in 1928, when the Democrats nominated New York Gov. Al Smith, the first Catholic to head a presidential ticket. Smith ultimately lost to Herbert Hoover amid a fusillade of anti-Catholic sentiment, including insinuations that a “Papist” could not be trusted to buck the Vatican on issues of public policy. Although explicit bigotry against Catholics declined in the following years, many Americans still doubted whether their largely Protestant nation would ever overcome its prejudices. Polite discourse in many places still permitted the suggestion that a Catholic might place loyalty to the pope over obedience to the Constitution (as today anti-Mormon prejudice remains surprisingly open).

In August 1960, after Kennedy had won the Democratic nomination for president, a flood of anti-Catholic literature reminiscent of the anti-Smith pamphlets of 1928 began circulating through the Bible Belt. In September, a group of 150 Protestant ministers partial to Richard Nixon put out a statement declaring that Kennedy’s religion was fair game. Calling themselves the National Conference of Citizens for Religious Freedom, the signatories included the prominent best-selling pastor Norman Vincent Peale, whose imprimatur gave the group authority and publicity. (Peale soon disassociated himself from the group.) These provocations persuaded Kennedy to tackle the slander that as a Catholic he would put private faith above public duty.

He did so in a speech to a different (though also unfriendly) group of ministers in Houston on Sept. 12. Confident that a majority of voters, including Protestants, would embrace his secular message, Kennedy had the address televised live on a statewide hookup. In no uncertain terms, he declared that “the separation of church and state is absolute.” Without any of the sort of meek protestation of piety that we now routinely hear from candidates, he continued:

I believe in a president whose views on religion are his own private affair, neither imposed by him upon the nation or imposed by the nation upon him as a condition to holding that office. I would not look with favor upon a president working to subvert the First Amendment’s guarantees of religious liberty. Nor would our system of checks and balances permit him to do so. And neither do I look with favor upon those who would work to subvert Article VI of the Constitution by requiring a religious test—even by indirection—for it. If they disagree with that safeguard, they should be out openly working to repeal it.

After Kennedy finished the speech, the ministers bombarded him with questions, many skeptical of his sincerity. When asked if the Vatican had approved his statement, Kennedy said that no such approval was necessary. When asked what he would do if church officials tried to influence his position on a matter of policy, he said in effect he would tell the clerics to butt out.

The speech didn’t quite put the issue to rest. Anti-Catholic demagogues continued to raise it (though Nixon, sensing the issue was a loser, steered clear). In areas where such prejudice was acute, JFK would fare poorly in November. But the speech muted the issue for the rest of the fall, made it clear that Kennedy held the moral high ground, and probably reassured a certain number of voters combating their own atavistic prejudices. The Kennedy campaign clearly considered the talk a success, editing the footage of it for distribution as campaign ads.

For a generation afterward, cultural change conspired with a new wave of Supreme Court jurisprudence to shore up popular support for Kennedy’s understanding of religious freedom. At the heart of this understanding was the notion, as Kennedy said in his Houston speech, that the “public acts” of a president (or any public official) “are responsible to all groups and obligated to none”—that a president’s policy decisions, even if informed somehow by religiously instilled values, had to be potentially acceptable to anyone, regardless of doctrinal belief.

This is quite different from the implausible scenario that Santorum conjures up of liberals barring the devout from holding office or from so much as mentioning their beliefs. Yet since the political mobilization of the religious right in the late 1970s, it has become increasingly common to hear charges that religion is somehow under threat—that Kennedy and his liberal heirs would create a country where, as Santorum said, “faith is not allowed in the public square” (or, as Romney put it, that they would seek “the elimination of religion from the public square”).

The vagueness of the recurrent phrase “the public square” in these Republican talking points reveals some of the problems with their arguments. Liberals—and a half-century of Supreme Court jurisprudence—do of course support the idea that the Constitution forbids government from subsidizing or privileging religion. But is there really anyone out there who contends that politicians can’t be religious or should never talk about God? “I do not intend to apologize for these views to my critics of either Catholic or Protestant faith,” Kennedy said in his speech, “nor do I intend to disavow either my views or my church in order to win this election.” Clearly, Kennedy didn’t think presidents had to be atheists.

There is one candidate for president this year who understands why Kennedy’s secular vision allows religion to thrive in America without unconstitutionally offering religious views government endorsement: Barack Obama. “Democracy demands that the religiously motivated translate their concerns into universal, rather than religion-specific, values,” he said in 2006, in his own Kennedy-style speech on church and state. “It requires that their proposals be subject to argument, and amenable to reason. I may be opposed to abortion for religious reasons, but if I seek to pass a law banning the practice, I cannot simply point to the teachings of my church or evoke God’s will. I have to explain why abortion violates some principle that is accessible to people of all faiths, including those with no faith at all.”

Fortunately, Obama’s religious views could never become a controversial political issue.