The fondest hope of al-Qaeda, the Islamic State, and other terrorist groups is to convince their followers that the world is divided into Dar al-Islam (the House of Islam) and the Dar al-harb (the House of War), and that the job of pious Muslims is to wage unrelenting war on “kafirs” (unbelievers) who refuse to accept the teaching of the Prophet. By going out of their way to denigrate Muslims, some leading Republicans are playing right into the terrorists’ hands.

As former Bush speechwriter Michael Gerson has noted, the list of Republicans who have insulted Muslims is a long one, and growing longer all the time. It starts with some of the contenders for the 2012 Republican nomination. Newt Gingrich warned that sharia law — i.e., the religious law of Islam, which is similar to the religious laws of Christianity or Judaism (from which Islam is derived) — is “a mortal threat to the survival of freedom in the United States and the world as we know it.” Herman Cain first said that he would not appoint any Muslims to his administration, then said he would so but only if they took a special loyalty oath.

This noxious theme has been carried on by some of those contending for the 2016 GOP nomination. Bobby Jindal has warned that Muslim immigration to the U.S. amounts to “colonization” and an “invasion,” and has said that the idea of a Muslim president is an “absurd hypothetical.” Before exiting the race, Scott Walker said there are only a “handful of reasonable, moderate followers of Islam who don’t share the radical beliefs that these radical Islamist terrorists have.” Mike Huckabee has called Muslims who commit violence after Friday prayers “uncorked animals.”

Donald Trump, the Republican front-runner who has previously described Mexican immigrants as “rapists” and “murderers,” did not correct a questioner at a town hall meeting who said, “We have a problem in this country, it’s called Muslims. Our current president is one.” Ben Carson, who is polling in second place behind Trump, has flatly rejected the idea that a Muslim should ever become president, saying, “I would not advocate that we ever put a Muslim in charge of this nation.” Apparently he’s never heard of the Constitution’s Article VI: “No religious test shall ever be required as a qualification to any office or public trust under the United States.”

This is nothing more than rank bigotry of the kind that once confronted Catholics who sought the nation’s highest office. Before John F. Kennedy won the presidency in 1960, there were many dark insinuations that Catholics were guilty of dual loyalties because they followed the Pope and therefore they could not follow the Constitution. Similar accusations of “dual loyalties” have long haunted American Jews who are accused by anti-Semites of being disloyal to the United States because they support the state of Israel. More recently, Mitt Romney faced some degree of opposition, especially from evangelicals, because of his Mormon faith. Now it is the turn of Muslims to feel the wrath of the intolerant.

Needless to say — although perhaps it bears repeating — very few Muslims support acts of violence carried out in the name of their faith. According to a Pew Research Centre survey in 2013, “Roughly three-quarters or more Muslims reject suicide bombing and other forms of violence against civilians.” Only about 10 percent of Muslims support terrorism, and of course even fewer of those — well under 1 percent — actually try to carry out attacks. That still means there a significant number of terrorist sympathizers out there — more than 100 million out of an estimated 1.2 billion Muslims in the world —so we in the West have real cause for concern about terrorist attacks, even if the most numerous victims of Muslim terrorism are fellow Muslims.

But pretty much the worst way to go about fighting Islamic terrorism is to declare that we think that all Muslims are terrorists or that we should wage war on Islam. This is a formula for futility and failure. The War on Terror must be fought and won by mobilizing the vast majority of moderate Muslims to more actively resist the siren song of the extremists, something that is currently being done from Egypt to Afghanistan. Those giving vent to anti-Islamic rhetoric are providing the best recruiting tool that jihadists can possibly have, because it confirms their claims that it is impossible for Muslims to live in peace alongside non-believers.

President George W. Bush understood this. It is why in his Sept. 20, 2001, address to a Joint Session of Congress, he said, “The terrorists practice a fringe form of Islamic extremism that has been rejected by Muslim scholars and the vast majority of Muslim clerics — a fringe movement that perverts the peaceful teachings of Islam.”

Mainstream candidates such as Marco Rubio and Jeb Bush have taken a similar line this year, yet their analysis is getting rejected by a disturbingly large minority of Republicans who think it is “politically correct” nonsense. Republicans who flirt with anti-Islamic bigotry are not only doing great damage to their political party. They are doing great damage to the United States as it struggles to defeat the forces of violent Islamist extremism.