“I like it. It’s making fun of ISIS which is a good thing,” Irfan Mansor, a man who identified himself as Muslim, wrote on the BBC Two Facebook page. “The whole point of satire is to bring people down to a level. If you can mock something, you’re not scared of it. ISIS want to be feared. Don’t give them that.”

Several scholars of Islamist radicalism echoed that view, saying that comedy was a potent weapon because it denies the Islamic State the approval it so desperately craves.

“We think nothing when the Ku Klux Klan or the Nazis are satirized, so why not ISIS?” asked Shiraz Maher, deputy director of the International Center for the Study of Radicalization at King’s College London. “ISIS wants to be taken seriously as an actor and state, they want approbation, and comedy denies them that, and takes away their shine.”

A BBC spokeswoman, Kate Toft, said the broadcaster was not commenting on the show “other than to say that it’s satire and the BBC has a rich history of satire.”

“Revolting,” the show on which the sketch aired, is the brainchild of Jolyon Rubinstein and Heydon Prowse, who met at an elementary school in North London and relish using a mix of acerbic humor, gags and pranks to puncture the hypocrisy they see in politics, business and religion.

The two men attracted the ire of pro-Israel groups a few years ago when they appeared in a comedy sketch in which they impersonated building contractors and told London store owners their land would be taken to make way for an extension of the Israeli Embassy.

Now they are defending “Real Housewives of ISIS,” saying that religious fundamentalism is fair game for satire. “It’s important not to pull your punches in satire,” Mr. Prowse told the British newspaper i. “You have to be fearless or it undermines your credibility.”