The magazine, which will still be available for purchase on periodical racks on Walmart stores, has been a focus of the nonprofit group for years. In 2015, the organization started a campaign to get stores to shield Cosmopolitan’s headlines and covers behind blinders or wraps similar to those that frequently cover pornographic material.

At that time, it worked with Victoria Hearst, the granddaughter of William Randolph Hearst, who founded Cosmopolitan’s publisher, the Hearst Group. The joint effort appeared to be successful.

Ms. Hearst, who now runs a “Cosmo Hurts Kids” campaign aimed at stopping the sale of the magazine to children under 18, was not involved in the center’s current push, according to according to Haley Halverson, the organization’s vice president for advocacy and outreach.

The group, which was founded in 1962 and was previously known as Morality in Media, has continued to focus on Cosmopolitan in part, Ms. Halverson said, because the magazine was “targeting young girls” with its messaging.

“A young teenager who first picks up Cosmo is going to be attracted to the bubble gum pink cover and to stories about Selena Gomez and One Direction,” Ms. Halverson said. “But within the covers, Cosmo is filled with extremely explicit articles that detail things like sexting, pornography, group sex, public sex and other forms of risky sex that actually a lot of young girls today are being pressured to do before they’re ready.”

Ms. Halverson also said the group viewed its efforts as especially important in the midst of the continuing conversation around sexual harassment that was sparked by the #MeToo movement.

“Cosmopolitan really likes to wrap itself up in its faux feminist mystique where they’re claiming that because they’re talking about sex, it’s liberating to women,” she said. “But it’s time to raise the level of discourse and say, ‘Well, are they talking about sex in an actually empowering or productive way?’”