I think because churches are completely irrelevant to the legal process of the marriage (they're not actually needed for anything - people just choose to use them a lot of the time), they wouldn't be compelled to sign a marriage licence of a couple they don't support. The actual ceremony is just that. Actually meaningless when it comes to the legal status of a marriage. I think that's a good balance of protecting a religious right and the interest of the public. Nobody has to get married in a Catholic church or have the license signed by a church official from some other religion.Does anyone know how marriage in a church works from a legal basis? You get a marriage certificate, which is the legal binding document and I thought the priest pretty much acted as a notary. The actual ceremony has nothing to do with government or legality. So I would think, at most, the court could force a priest to not be discriminatory about who he oversees the handling of the marriage certificate for. I don't think they could possibly force him to hold the ceremony.
I could be totally wrong on the my assumptions of how it all works though.
However, government employees, notaries, etc., are actually necessary for the license. And as working for the government, they are required to uphold the law. They take an oath to the constitution, not a religious text. So as long as they can verify the couple coming in are eligible for marriage based on state and/or federal law, they have a duty to marry them.