Churches may be “open door”, but they are for sure NOT “open season”. These protestors have no reason to be poaching. One little-noticed provision of the First Amendment, the very first clause, is “establishment of religion, or prohibiting the free exercise thereof”, before freedom of speech, or the press, or people PEACEABLY to assemble, or petitioning the Government.
Churches are private property. They control who can come in and who can get kicked out.