Yes, houses of worship are open to the public. But not all that goes on in the church is open to all. Some of the pastors I know will not marry a couple unless at least one is a member of his congregation or denomination.
I know will = I know pastors that will
Something happened during my editing.
By the way, there are a number of reasons why a pastor might refuse to marry a party of two or three or more persons who desire a marriage license and civil contract. Perhaps:
-- One of the parties is a drunk.
-- One of the parties is in debt.
-- One of the parties is immature.
-- One of the parties is Jewish and the other Catholic.
-- One of the parties is an atheist.
-- One of the parties is a florist.
-- The parties demand the preacher bake them a cake.
-- They want a red swastika decoration on the cake.
-- One of the parties is white, red-headed, and left-handed.
-- One of the parties looks funny.
-- One of the parties doesn't believe in global warming.
-- There are three parties.
Which of these involve civil-rights law and prohibitions on discrimination?
That is true. All denominations have their own "house rules" that stem from their doctrine plus tradition. My husband will not marry a couple unless they have at least one or two counseling sessions. There is no law that says he has to require that. It's a matter of personal belief and religious obligation. A pastor must have freedom of conscience under God's will. They will not move from that freedom if they are truly committed to the Lord.