The U.S. Supreme Court on Monday rejected an appeal from a right-wing provocateur who had sought to post throughout Metro advertisements depicting the Prophet Muhammad.

Pamela Gellar and her organization, American Freedom Defense Initiative, had argued that Metro’s refusal to run the ads violated the right to free speech.

The “Support Free Speech” ads Ms. Gellar intended to run included a drawing of the Prophet Muhammad that was the winning entry in an art contest her organization had sponsored.

Islam forbids any depiction of Muhammad, the religion’s founder.

Metro rejected the ads, citing its 2015 policy banning all issue-oriented advertising.

The regional transit agency for decades had allowed political and religious ads. A survey in 2015 showed that 58% of riders dislike issue-oriented ads, and Metro then banned all advertisements that aim to influence the public, including on issues of public policy and religion.

The U.S. Court of Appeals for the D.C. District ruled against Ms. Gellar, deciding that Metro is not a public forum and its issue-oriented ban is acceptable because it doesn’t discriminate against a particular viewpoint.

The Supreme Court justices declined to hear the case without comment, but the issue isn’t going away soon.

The Archdiocese of Washington also has appealed to the high court, challenging Metro’s refusal to run an ad during the Christmas season on the religious meaning behind the holiday. The ad depicted shepherds and sheep on a hill, and suggested the season’s “perfect gift” was church services and charitable giving.

Metro officials said that advertisement also ran afoul of the issue-oriented ban.

U.S. District Court in Washington ruled against the archdiocese.

In its appeal, the archdiocese said its ads were no different than those advertising yoga, which the Catholic church argued has historical links to Hinduism and Buddhism, and those for a Christian radio station — both of which Metro allows.

“Viewpoint discrimination is always a matter of grave concern, but viewpoint discrimination against religious speech is particularly pernicious,” the archdiocese argued, according to court records.

Robert Tuttle, a law professor at George Washington University, doubted the church will have any better luck than Ms. Gellar.

“There’s enough law out there to cover the matters, and no clear split among the circuits would push the court toward taking one or both of those cases,” Mr. Tuttle said.

Eugene Volokh, a professor at UCLA School of Law, said Ms. Gellar’s case had been remanded back to the district court, so the justices could be waiting to take up the issue at a later time.

“The odds are almost always against the court granting any particular case, but it’s certainly possible that the court will be more interested in the archdiocese petition than in this one,” Mr. Volokh said.

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