The day after two gunmen were killed by police while trying to shoot their way into a Garland, Texas community center hosting a Mohammed cartoon contest, reformist American Muslim activist Zuhdi Jasser appeared on Fox News not only to condemn the attack but to unconditionally affirm the right to free expression—including the right to insult Islam—and praise defiance against blasphemy bans.

What Jasser graciously did not mention was that the people whose speech he was defending—contest organizers and anti-Islam polemicists Pamela Geller and Robert Spencer—had viciously attacked him in the past. In a 2011 article published by the right-wing website The American Thinker in response to Geller’s screed on the same site, Jasser documented the duo’s smear campaign in which he was sometimes dismissed as a faux Muslim and sometimes denounced as a camouflaged extremist practicing taqiyya, the doctrine which supposedly allows Muslims to lie in the cause of Islam.

This sordid episode is typical of the way Geller and her comrade-in-arms Spencer, co-founders of the American Freedom Defense Initiative, conduct their misnamed “anti-jihadist” battle. It is also a good example of why the two are no heroes for free speech. No, Geller did not “provoke” the terror attack in Garland, as a number of pundits (and even the New York Times editorial board) have deplorably suggested; her cartoon contest is not the moral equivalent of the attack, and she does not need to apologize for the exercise of her First Amendment rights or for the terrorists’ actions. She does, however, have to answer for a lengthy record of peddling anti-Muslim hysteria, targeting Muslims’ First Amendment right to worship, smearing innocent people as jihadists, and even excusing the slaughter of Muslims in the former Yugoslavia. We cannot allow terrorists to curb our speech; but we also cannot allow them to turn hatemongers into heroes.

Whatever valid concerns Geller, Spencer, and their allies may raise about political Islamism wind up being eclipsed by the fact that they not only conflate Islamist radicalism with all Islam but make disturbingly little distinction between criticism of Islam and hostility toward Muslims.

In a contentious interview with CNN host Alisyn Camerota Monday, Geller indignantly denied that she paints Islam “with a broad brush,” declaring that she is “anti-jihad” and “anti-sharia.” But for the most part, she and Spencer make almost no secret that they regard radical Islam as indistinguishable from Islam itself.

Spencer, a prolific author who has a degree in religious studies and whose tone is more judicious than Geller’s, does not quite state outright that non-extremist Islam is impossible. Nonetheless, he calls Islamic reform “quixotic” and “virtually inconceivable,” and sweepingly describes the faith of “millions” of Muslim immigrants in the West as “absolutely incompatible with Western society.” When America’s first Muslim congressman Keith Ellison (D-Minnesota) chose to use a Quran in his swearing-in ceremony, Spencer flatly stated that “no American official should be taking an oath on the Qur’an.” His 2005 best-seller, The Politically Incorrect Guide to Islam (and the Crusades), has such chapter titles as “Islamic Law: Lie, Steal and Kill.”

Critics accuse Spencer of cherry-picking and distortions. While these charges often come from sources with biases of their own, there is no doubt that his account of Islamic history is blatantly one-sided. Thus, he tries to rebut the “PC myth” that Jews in the Middle Ages fared better under Islamic rule than in Christian Europe by quoting from a 13th Century papal bull that affirmed the rights accorded to Jews—but fails to mention the many expulsions of Jewish communities from European countries and glosses over crusader massacres of Jews.

When Spencer writes about moderate Muslims, it is invariably to disparage them as deluded, insincere, or irrelevant. His targets include reformist Muslims who are strongly critical of radical Islamism and have themselves been accused of being Islamophobic shills: Jasser, self-styled “Muslim refusenik” Irshad Manji, Sufi Muslim convert Stephen Schwartz. They also include Kurdish fighters battling the Islamic State: last October, a Spencer post on his site, JihadWatch, reported a Kurdish woman’s suicide bomb attack on ISIS troops in a besieged town under the jeering headline, “Kurdish Muslima carries out moderate jihad/martyrdom suicide attack against the Islamic State,” and sneered at the idea that “the foes of the Islamic State are all moderate.”

Spencer ostensibly disavows bigotry; yet a 2006 JihadWatch post,—written by the site’s co-administrator Hugh Fitzgerald but posted by Spencer himself—suggests that the most peaceful, non-violent, and even secularized Muslims are still a danger to the West as long as they have not explicitly renounced Islam, because either they or their children may revert to a more militant form of the faith.

Both Spencer and Geller relentlessly hype the Muslim peril in the U.S. Every violent crime by a Muslim becomes a one-person jihad, from a mentally ill Bosnian teen’s shooting spree at a Salt Lake City shopping mall to a drug addict’s meth-fueled rampage assaulting customers and staff at a Seaside, California Walmart.

In 2011, Geller sounded the alarm about “Vehicular Jihad in Arizona,” where a man named Ajaz Rahaman was found dead after crashing his SUV into a shopping center storefront and hitting three cars in the parking lot. Later, Geller apparently scrubbed the story from her site when it was confirmed that Rahaman, a respected ob-gyn, had died of a massive heart attack while driving. The deleted post, preserved in a blog feed archive, also mentioned a “vehicular jihad” incident in San Diego in which a taxicab driven by an Egyptian immigrant jumped a curb and injured 35 people; Geller forgot to mention that the police determined the cabdriver had fallen asleep at the wheel.

Homicidal (and suicidal) non-Muslims can be recruited to the cause as well. In 2007, Geller harped obsessively on the notion that Virginia Tech mass shooter Seung-Hui Cho, a Korean national and a Christian, was a secret jihadi because of the mysterious “Ismail Ax” tattoo on his arm. Two years earlier, Spencer was one of the bloggers flogging the theory that Joel Hinrichs, a University of Oklahoma engineering student who killed himself by detonating a homemade bomb in his backpack near the campus football stadium during a game, was a Muslim convert and had planned a suicide bombing inside the stadium. This speculation was based on these incredibly incriminating clues: Hinrichs had recently grown a beard, had lived a few blocks from a mosque, and had a Pakistani roommate.

This Muslims-under-the-bed paranoia also drives distortion-riddled reports about the alleged encroachment of “sharia law” in America—which can mean nothing more than utterly innocuous accommodations for practicing Muslims such as ritual foot baths on university campuses and at airports.

Take the “sharia courtroom” scandal in 2012, in which a Muslim judge in Pennsylvania was said to have let a Muslim immigrant off the hook for assaulting an atheist who had marched in a local Halloween parade dressed as “Zombie Mohammed.” The only grain of truth in this story was that the judge, Mark W. Martin, had quite inappropriately lectured the victim for abusing his First Amendment rights before dismissing the harassment charge for lack of evidence. But Martin, a Republican and an Iraq war veteran, was (as he confirmed to the media) a churchgoing Lutheran; the confusion was based on a misheard line in the audio of the court session.

Undeterred, Geller continued to insist that Martin was a “sharia judge” who had declared himself a Muslim in the court hearing and was probably lying about it in the aftermath—because, of course, Muslims lie.

Geller herself has a rather strained relationship with the truth. In 2011, she agreed to settle a defamation suit by removing from her site several posts suggesting—with no evidence—that Columbus, Ohio attorney Omar Tarazi had ties to the terrorist group Hamas. Tarazi was the attorney for the parents of Rifqa Bary, a runaway Ohio teen who became a cause célébre for the “anti-jihadist” set when she took refuge with a pair of Florida pastors she had met online, claiming that her Muslim parents were going to kill her for converting to Christianity.

If Muslims in the Geller/Spencer universe are always presumed guilty of jihadism, any non-Muslim seen as too soft on Islam is branded a “dhimmi”—a term that, historically, denotes the subject status of Christians and Jews under Muslim rule. Even Bernard Lewis, preeminent Middle East historian and longtime critic of Islamic radicalism, once ended up on the “Dhimmi Watch” wall of shame on Spencer’s site. Lewis has weathered his share of attacks for alleged anti-Islamic and anti-Arab views. But he has run afoul of the “anti-jihadists” for taking too positive a historical view of Islamic civilization. Geller, meanwhile, has castigated Lewis in more colorful terms as an “apologist for Islam” and even for “Islamic Jew-hatred.”

Another strong critic of Islamism, Michael Totten, an award-winning foreign correspondent whose work has appeared in such publications as Commentary and The Wall Street Journal, has been targeted by Geller for writing too sympathetically about Bosnian and Kosovar Muslims.

“I got on the hit list of Pamela Geller and her flock of honking geese when, while reporting from Bosnia and Kosovo, I wrote about Serbian ethnic cleansing and war crimes,” Totten told me in an email. “She insists not only that Serbian ethnic cleansing didn’t occur—never mind that I know some of the victims and visited some of the ethnically cleansed areas in person—but also that ‘every major US paper in 1999’ supposedly ‘debunked’ the ethnic cleansing that every knowledgeable and serious person knows happened. The woman lives in an alternate universe.”

Totten’s run-in with Geller highlights another troubling aspect of her views: a propensity for Bosnian Muslim genocide denial and for valorizing Serbian mass murderers as leaders of anti-jihadist resistance. (“The Serbs dared to fight. That’s what this is all about,” she wrote in a 2011 post.) Spencer has generally stayed quiet on this issue, but one his closest associates, writer and academic Srdja Trifkovic, is not only a denier of Serbian war crimes but a former advisor to one of the accused perpetrators, Bosnian Serb politician Radovan Karadzic.

Kejda Germani, the Kosovar émigré writer who documented the Spencer/Trifkovic connection five years ago, wrote at the time that Spencer and his associates’ “shrill and unfortunately universally accepted identification with ‘the counter-jihadist movement’ is severely detrimental to the efforts of respectable intellectuals standing up to Islamofascism.”

In fact, what’s obfuscated by the hate is that some “anti-jihadists” do have legitimate points that are too often dismissed by liberal commentators in debates over Islam and Islamophobia.

It is true, for instance, that Islamist radicalism cannot be treated as simply a perversion of Islam when it is backed by scriptural passages and much Islamic theology. It is true that, at present, radical ideology is vastly more powerful and more mainstream in Islam than in other major religions, and even some clerics praised as moderates—such as Egyptian cleric Yusuf Al-Qaradawi—justify the death penalty for apostasy and homosexuality. It is true that troublingly large majorities of Muslims in many countries, including Afghanistan, Egypt, and Pakistan, support sharia law—the real, on-the-books version—and executions for religious and moral offenses. (It’s also important to note that Muslims in Turkey, Central Asia, and the former Yugoslavian states generally do not).

It is true that while American Muslims hold notably moderate views, radicalization is a real problem. (Consider the career of radical imam Anwar Al-Awlaki, killed in a U.S. drone strike in 2011, who served a large congregation in Northern Virginia and preached at many other mosques before going to Yemen in 2004 to fight for Al Qaeda.) It is true that, as reformist American Muslim writer Asra Nomani argued in a recent essay in The Washington Post, the charge of “Islamophobia” often gets hurled at critics of Islamic extremism.

But treating Islam as a monolith, denying the possibility of reform, and demonizing Muslims en masse is not the answer. If Christianity and Judaism could transcend their scriptural and theological baggage once used to justify fanaticism and oppression, there is no reason to believe that Islam cannot do the same. Spencer has argued that Islamic reform has no theological foundation, but he ignores the work of such 20th Century thinkers as Mahmoud Mohammed Taha, who made the case for the abrogation of the Quran’s later, harsher texts by the earlier, more peaceful ones (rather than vice versa). Today, there are Muslim scholars who champion a revision of Islamic orthodoxy on everything from women’s rights to religious freedom. In 2004, over 2,500 Muslim academics from 23 countries signed a petition to the United Nations condemning “Sheikhs of terror” who use Islamic scriptures as justification for political violence.

This is why, while we must stand by Geller as a victim of an outrageous attack on fundamental speech rights, it would be a tragic mistake to treat her or Spencer as leaders in the fight against the radical ideology that has been called Islamism or Islamofascism.

In his 2011 response to their attacks, Jasser warned that “Geller’s and Spencer’s genre is headed in only one direction—declaring an ideological war against one-fourth of the world’s population and expecting to neutralize the Islamist threat by asking Muslims to renounce their faith.” It is, perhaps literally, a dead end.