The issue of politicians’ faith resurfaced last week after GOP presidential candidate Donald Trump did not challenge a supporter who said President Obama, a Christian, was Muslim. It was followed by Ben Carson saying he would not support a Muslim for president.

This prompted some strong rebukes from other candidates. In rare agreement, Democratic contender Hillary Rodham Clinton and Republican candidate Sen. Ted Cruz (Tex.) cited the U.S. Constitution, which says there shall not be a religious test to qualify for public office.

[Despite backlash, Ben Carson is not backing down from his opposition to a Muslim president]

Republican Mitt Romney, his party’s standard bearer in 2012, who is Mormon, tweeted:

But what about having no religion?

While there may not be a religious test, there is an irreligious test, at least in public opinion. Not believing in God is perhaps the greatest limitation to getting elected to public office, particularly at the national level.

On Capitol Hill, no lawmakers are openly atheist.

Barney Frank was the first openly gay member of Congress – coming out long before the societal sea change in support for gay rights. But it wasn’t until he retired that he spoke openly about not having religion.

Yet even Frank, the former Democratic congressman from Massachusetts, has eschewed the label “atheist.” And while he jokingly referred to himself as a “pot-smoking atheist” during an appearance on HBO’s” Real Time with Bill Maher” in 2014, he has advised nonbelievers not to use the term atheist because it still has a negative connotation.

“I never expressed the fact that I was not a believer in any theistic approach because it was never relevant,” he said in April, urging other nonreligious politicians to keep it to themselves.

That seems to be a position shared by the few other politicians without a declared religious affiliation. Rep. Kyrsten Sinema (D-Ariz.), does not have a religion, but she will not call herself an “atheist.”

“I think a person’s religion is a private and personal matter,” she told the Loop in a statement. “I am not a member of a faith community. What I think is great about America is that we have the freedom to worship as we chose, or not worship at all, and government has no say in that choice whatsoever.”

There’s also Sen. Bernie Sanders (I-Vt.). The Democratic presidential candidate who has inspired a strong grassroots following this summer, is also, in his words, “not much into” organized religion. But he considers himself spiritual. His beliefs, if they must be labeled, would better be described as agnostic.

Meanwhile, these conversations around the importance of faith – and what kind – in politicians comes as the world’s most influential religious leader visits the U.S. capital and addresses its policymakers. Pope Francis will be the first ever pontiff to address Congress, where about one-third of lawmakers are Catholic. And most members of Congress are Christian.

Getting elected in America as a non-Christian is hard. Getting elected without any religion is harder.

In a May 2014 Pew Research survey, atheism was the most disqualifying factor for a potential presidential candidate. More than half said they’d be less likely to vote for someone who didn’t believe in God.  And another Pew poll in July 2014 found that of all religion-related groups, atheists and Muslims were viewed the most negatively by Americans.

That might explain why Roy Speckhardt, executive director of the American Humanist Association, claims at least two dozen currently serving members of Congress are atheists, but are afraid that “if they were open about their lack of belief in God it would prevent them from getting re-elected.”

Their internal justification is that not believing – unlike believing – is not a huge part of their identity, so standing up for it wouldn’t be worth jeopardizing what they consider a larger contribution through public service.

And while there is a downward trend in people identifying with a specific religion, faith remains a huge part of the American fabric.

Ron Reagan Jr., the liberal son of the late conservative icon Ronald Reagan, is an avowed atheist, appearing in a controversial commercial this year for Freedom From Religion Foundation where he states he’s “not afraid of burning in hell.”

In an interview after his father’s death in 2004, Reagan was asked by Larry King whether he’d want to run for public office. The younger Reagan said no.

“I’m an atheist. So there you go right there,” he said. “I can’t be elected to anything because polls all say that people won’t elect an atheist.”