According to the First Amendment, the U.S. government can take the action of preventing public schools from leading children in prayer. The First Amendment prohibits the government from establishing a religion, which has been interpreted to mean that public schools cannot promote or lead organized prayer, thereby ensuring the separation of church and state.
The other options listed—keeping the media from making negative statements about public officials, banning video games and music that offend people, and stopping people from posting offensive things on social media—would violate the First Amendment's protections of free speech and expression.