Back when in 1870 or so when all my Catholic ancestors came to the USA from Rheinpfalz, Germany, the Catholic Church was opposed to the state institution of civil marriage. It was Bismarck who had pushed it through: licensing gave the German State the power to control something it clearly had no right to control, the institution of marriage.
I have an ancestor there who had to post a bond in the equivalent in today's money of about $20K to get a license to marry. His father had to mortgage the family grist mill to come up with the money. It was returned after either spouse died or they remained married for a specified time, about three years. But, of course, the government had use of the bond money all that time and returned only the face value of that bond.
Interesting stuff and could explain why so many moved into the high country, just shacked up or married with the local Cherokee who didn't require such bonds.
So you want Muslim clerics and gay clergy, and Mormons, along with priests to decide what is a legal marriage?