There is a paradox to the recent terrorist attacks in Paris. As it claimed responsibility for them, Islamic State said they were meant as a strike against European depravity. Yet the perpetrators of the attack were apparently no puritans.

The Islamic State message called Paris “the capital of prostitution and obscenity” and the rock concert at the Bataclan, where most of the victims died, a “profligate prostitution party” for “hundreds of apostates.” That’s standard rhetoric for the group, which has been known to execute people for smoking, drinking or homosexuality. It’s supposed to have a low tolerance of vice, though slavery and rape are tolerated, encouraged, if the victim is an infidel.

Yet after the Paris attacks, witnesses reported seeing one of the top suspects — Abdelhamid Abaaoud, who was later killed by French police — sitting outside his apartment drinking and smoking pot with his friends. He was apparently known on his street as someone who liked to hang out.

Even if these reports carried by tabloids are false, it is an established fact that Salah Abdeslam, the subject of a Belgian manhunt that has paralyzed Brussels since the weekend, and his brother Brahim, who blew himself up outside a Paris restaurant, owned a gritty bar in Molenbeek, Brussels, until two months before the attacks. The bar, Les Beguines, sold alcohol (it even had a sign for Jupiler beer above the entrance). Neighbors complained of frequent fights and loud music, and in August, police raided the establishment to find half-smoked joints in ashtrays and drugs in customers’ pockets. Les Beguines wasn’t a paragon of Islamic purity, and neither, by all accounts, were its owners.

After the August raid, police threatened to close the place down. The Abdeslams missed their chance to object, and on Nov. 5, Les Beguines was closed for five months; but by then, the brothers had sold the bar — and apparently immersed themselves in attack plans.

Much is often made of the fundamentalist puritanism of Islamic State and other terror groups, such as al-Qada. War photographer Teun Voeten, who had long lived in Molenbeek, wrote in a recent piece for Politico:

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“Over nine years, I witnessed the neighborhood become increasingly intolerant. Alcohol became unavailable in most shops and supermarkets; I heard stories of fanatics at the Comte des Flandres metro station who pressured women to wear the veil; Islamic bookshops proliferated, and it became impossible to buy a decent newspaper.”

Yet the bothers Abdeslam were not the kind of guys who pressured merchants to stop selling alcohol. They sold it — and perhaps other substances — themselves.

The terrorist organizations may call themselves Islamic — and right-wingers both in the U.S. and in Europe may pressure political leaders to use the denomination less sparingly — but the fighters they recruit in the Muslim communities and on the Internet are, by their own supposedly strict standards, apostates. They are petty criminals, drug experimenters, prostitutes.

In a study of Belgian and Dutch converts joining Islamic State, published earlier this year, Marion van San of Erasmus University in Rotterdam noted:

“The converts introduced in this Research Note were all under the age of thirty, came from lower- or lower-middle-class socio-economic backgrounds and had a low or medium level of education. Many of them, especially the girls, had a problematic childhood and adolescence. A common theme throughout their lives is that almost all of them were, in one way or another, abandoned by their fathers at a young age. Most of them used alcohol and drugs as teenagers and frequented nightclubs, while some of them were involved in prostitution or petty crime. Their conversion was often a means to escape their former lifestyles. Some girls left for Syria because they thought their sins would be forgiven.”

The young men and women interviewed by van San were not even from Muslim families, and all they knew about Islam initially came from the social networks, but they all ended up in Syria. The radicalization of young people from Muslim families often follows the same pattern — first a lifestyle inconsistent with any fundamentalist values, then a supposed conversion. Young women who used to smoke, drink and go out with men suddenly start wearing a niqab. Kids involved in petty crime turn serious and saintly.

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The phenomenon is by no means new. In a 2008 paper on al-Qada as a youth movement, Islam expert Olivier Roy wrote:

“The Europeans in Al Qaeda tend to take one of two routes to conversion: there are those who have pursued a personal path and joined AQ after having converted in a 10 mosque, and those who followed their Muslim ‘buddies’, when, often after a story of petty crimes, they decide to ‘go for action’, usually under the influence of a group leader, seen as a guru.”

Many are radicalized in prison after being put behind bars for non-terrorist crimes, as was Amedy Coulibaly, who held hostages in a Paris kosher supermarket in January. He became an “Islamist” after meeting an al-Qaida recruiter while serving a six-year sentence for armed robbery.

A desire to leave dreary lives, bad habits and disapproving families behind, wipe the slate clean and perhaps go out in a blaze of glory has little to do with any religious teaching: It’s only human. These street-toughened young people may, of course, be naive enough to buy the promise of heaven for martyrs wearing suicide belts; more likely, they’re just looking for the baddest gang around or just comradeship for the sake of some remote goal.

With or without Islam, these young people would probably find a cause to fight and die for. Islamic State certainly competes for them with crime syndicates. In a recent interview with NBC News, Giovanni Gambino, son of a prominent U.S. mafioso, said this:

“The world is dangerous today, but people living in New York neighborhoods with Sicilian connections should feel safe. We make sure our friends and families are protected from extremists and terrorists, especially the brutal, psychopathic organization that calls itself the Islamic State.”

Islamic State and other Middle Eastern terror groups also equip neighborhoods with “connections” for their “protection.” They are crime syndicates masquerading as religious organizations; it enables them to sugar-coat their stark offerings to young people in a kind of idealism.

Jobs and education programs for neighborhoods such as Molenbeek, where half of young people are unemployed, and perhaps a higher tolerance for relatively harmless offenses, such as selling marijuana, would do more to put Islamic State out of business in Europe than a focus on Islam as a supposedly dangerous religion or curbs on immigration. Sure, some young people would still be drawn to violent adventures and charismatic radical preachers, regardless of their creed. Yet it’s hard to imagine the Abdeslam brothers as true believers in any religion. Had it not been for the police raid, they might still be hanging out at their rough bar with joints in their hands.

 Leonid Bershidsky, a Bloomberg View contributor, is a Berlin-based writer.