The founders of this nation recognized Islam as one of the world’s great faiths. Incredibly and disgracefully, much of today’s Republican Party disagrees.

Thomas Jefferson, whose well-worn copy of the Quran is in the Library of Congress, fought to ensure that the American concept of religious freedom encompassed Islam. John Adams wrote that Muhammad was a “sober inquirer after truth.” Benjamin Franklin asserted that even a Muslim missionary sent by “the Mufti of Constantinople” would find there was “a pulpit at his service” in this country.

Indeed, the Constitution states that “no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States.” Some of the GOP candidates for president, however, simply do not care.

Ben Carson said Sunday that he believes Islam to be inconsistent with the Constitution and therefore he could not support a Muslim candidate for president. “I would not advocate that we put a Muslim in charge of this nation,” he told NBC’s Chuck Todd. “I absolutely would not agree with that.”

A campaign spokesman, seeking to clarify Carson’s remarks, effectively doubled down by claiming there is a “huge gulf between the faith and practice of the Muslim faith and our Constitution and American values.”

Carson is dead wrong, but at least he seems sincere about it. Louisiana Gov. Bobby Jindal said he could only support a Muslim candidate “who will respect the Judeo-Christian heritage of America.” Sen. Rand Paul said a president’s faith should be irrelevant, but he understood many people felt otherwise because “we were attacked by people who were all Muslim.” And front-runner Donald Trump, when asked about the possibility of a Muslim president, wisecracked, “Some people have said it already happened” — a reference to oft-repeated lies about President Obama’s faith.

I was ready to offer rare praise for Sen. Ted Cruz, who rejected Carson’s outrageous view by pointing to the Constitution’s prohibition against religious tests. But then Cruz went on to say the United States should accept Christian refugees from the Syrian civil war but not Muslims, who might, after all, be terrorists.

There is an ugly undercurrent of anti-Muslim bigotry in this country, and the Republican Party panders to it in a way that the Democratic Party does not.

This rancid sentiment was on display at Trump’s town hall meeting in New Hampshire last week, at which a questioner began by stating a premise: “We have a problem in this country, it’s called Muslims. We know our current president is one. You know he’s not even an American.”

The man went on to say that these problematic Muslims “have training camps growing where they want to kill us. That’s my question, when can we get rid of them?”

Trump should have showed some backbone and told the man his worldview was based on paranoid fantasy. Instead, he made vague noises of agreement, or at least non-disagreement — “A lot of people are saying that. … We’re going to be looking at that and plenty of other things” — which kicked off a round of criticism from his campaign rivals.

But where were these high-minded, all-embracing Republicans when Trump and others, with no factual support, were casting doubt on Obama’s religion and birthplace? Leaving Obama aside, since he’s in a position to defend himself, where were the wise GOP elders when their party became a refuge for extremists spouting the worst kind of anti-Muslim rhetoric?

After the 9/11 attacks, George W. Bush did an admirable and important thing: He made clear that blame for the atrocity should not be ascribed to Islam itself but rather to a small group of radical fundamentalists.

Going forward, however, his administration was neither specific enough nor consistent enough about culpability for the terrorist strike. Warmongers found it politically useful to suggest involvement by Iraq, which had nothing to do with the attacks. Meanwhile, officials downplayed the fact that most of the attackers came from Saudi Arabia, considered a valuable ally.

This fuzziness, I believe, helped give some Americans the impression that the United States was at war not with small and vicious bands of jihadists but with Muslims more broadly. Democrats almost invariably pushed back against this dangerous misimpression. Republicans far too often did not.

On the campaign trail, GOP candidates are touting their own Christian faith in what can only be described as a literal attempt to be holier than thou. They should reread the Constitution, which says “no religious test” — not “only the religious test that I can pass.”

Eugene Robinson’s email address is eugenerobinson@washpost.com.