Separating "church" and "state" was one of the brilliant reasons our founders established the most successful government on record. Marriage needs to stay separate like it was at our countries beginning.
As the US doesn't need to know who and where citizens get baptized or are church members, they don't need to know who they get married to, where they get married, or even if they are married. This is a religious institution and it's governmental knowledge is not needed to govern our people.