Quite simply, the Constitution prohibits the state from interfering with the church, but does not prohibit the church from influencing the state.
And there is no limit whatsoever to what states may do in the realm of religious expression. The First Amendment ties only the hands of the federal government. Once again, this truth is hiding in plain sight.
“CONGRESS shall make no law …” Congress was prohibited from picking one Christian denomination and making it the official church of the United States (the Establishment clause) and flatly prohibited from telling the church what to do (the Free Exercise clause).
In fact, the real separation in the First Amendment is not between church and state but between the federal government and the individual states. The federal government is stringently forbidden to extend its tyrannical little hand into the operation of religious liberty in the individual states. States have unfettered religious liberty under the Constitution, and can do whatever they and their state constitutions permit.
— Bryan Fischer, “Freedom From Religion Foundation Needs Grammar Lesson”, RenewAmerica