Whenever an act of horrific terror enrages the West, a predictable second act ensues. Furious commentators and activists on the right erupt with blanket denunciations of Islam, Muslims and their supposed plots to enslave us all under Shariah, urging that we ban the religion, stigmatize its faithful and restore the Judeo-Christian exclusivity of America. Sometimes a few even seek retribution in attacks on mosques, individual Muslims and anyone unfortunate enough to “look Muslim.”

Violent or merely loud, these are the useful idiots whose divisive blundering underscores the propaganda of al-Qaida, the Islamic State group and imitators around the world. They represent precisely the opposite of what we must do and say if we are to defeat Islamist extremism in all its manifestations.

Look behind the delusional murderers who actually carry out such crimes as the massacres at Charlie Hebdo and the Paris kosher market. What is their strategic objective? Not a military victory over the French army or even an atmosphere of fear in Paris. They seek to provoke a harsh crackdown on innocent Muslims, especially the young and unemployed, along with expressions of bigotry and discrimination—to highlight the simmering communal conflicts they hope to inflame into a “war of civilizations.”

So the extremists can only be grateful when anti-Muslim propaganda, repeated constantly in right-wing publications and broadcasts, casts them as the defenders of Islam rather than its defilers. Every time Islam is publicly defined as a religion of violence, the jihadis gain prestige. Their appeals become more persuasive to oppressed young Muslims—especially if no alternative is apparent.

Yet the narrative of endless conflict and implacable distrust is not only untrue—as we saw last week when Parisians of all faiths rallied together—but deeply destructive to traditional democratic values and strategically stupid.

Yes, we must protect the right to speak freely, including when the speech is offensive to religions and even to ethnic groups, without fear of violent responses. We must also protect the rights of religious and ethnic minorities—including the right to protest peacefully against offensive speech. That requires swift action against those who will conspire to maim, murder and terrorize—and the capacity, whenever possible, to neutralize those criminals before they act.

But Americans will need to do much more than surround ourselves with police, armies and intelligence services if we ever hope to overcome our extremist enemies. Effective counterterrorism demands a contrasting narrative of coexistence, respect, fairness and opportunity.

The elements of that political arsenal exist already—in the stories of Ahmed Merabet, the Muslim policeman who died heroically in Paris, and Lassana Bathily, the young Muslim employee who led Jews in the kosher market to safety; in the undeniable fact that the extremists murder hundreds of innocent civilians, overwhelmingly Muslim, every week; and in the secure, prosperous existence that millions of ordinary Muslim families have enjoyed in this country for decades, despite outbursts of prejudice and harassment.

We ought to note with pride that Muslims serve in the U.S. military and every branch of government, including two members of Congress, because the Constitution specifically bans any religious test for public office. (Certain figures on the religious right may need to be reminded, too.) Muslims should know that their holy days are routinely celebrated in the White House by presidents of both parties—even as all religions are subject to disbelief, criticism and even jeering satire in a free society.

The consensus among ordinary Muslims is well-known to pollsters of public opinion: By large majorities, here and abroad, they fear and disdain the violent extremists who have defamed their religion. Let’s at least stop trying to change their minds.