It's as far from a religious mode as you can get. It's no mode at all.There is no law that forces anyone to issue a marriage license.
That's a strawman. Nobody said there was such a law. The issue we are discussing is the hows and wheres of a state withdrawing completely from the act of licensing marriages. It is entirely within the states' powers to cease the practice of requiring a marriage license in order for two people to get married. On the other hand, if the the state's newly crafted mode of entering into legal marriage is 100% dependent on a religious mode, the state's law would run afoul of the constitution.