The New York Times has an editorial praising the Supreme Court's ruling that anti-gay protests at military funerals are speech protected under the First Amendment. Other Times editorials in the past have taken the position that the First Amendment protects both "animal cruelty videos" that include "depictions of animals being crushed or mutilated" and also "the sale of violent video games to minors." The Times has also, in the past, said that the First Amendment should allow Americans to provide "material support" to terrorist groups.
What the First Amendment doesn't protect, in the Times's odd view of it, is political speech in the form of campaign commercials funded by corporations or anonymous individuals. They are First Amendment absolutists over there, except when the speech threatens their own hold on the political discourse.