This week’s campaign is the latest in a long-running fight by Internet vigilantes to disrupt the Islamic State’s online propaganda.

“Basically, our work not only cripples their ability to spread propaganda, but also wastes their time,” a Twitter vigilante who goes by the screen name The Doctor told The New York Times in March.

The Islamic State has regularly used social media to spread its message, recruit fighters, and threaten “infidels” and other enemies. The insidious threat it represents appears to motivate Muslims like Mr. El-Baghdadi to fight the extremists at every tweet.