Nah...long before that! This road started the moment government started butting into the personal religious concern known as marriage.
It was landmark U.S. Supreme Court precedent Reynolds v. United States in 1878 that made separation of church and state a dubiously legitimate point of case law, but more importantly; it confirmed the Constitutionality in statutory regulation of marriage practices.
(See also: Late Corporation of the Church of Jesus Christ of Latter-Day Saints v. United States, 1890.)
No man can become a law unto himself under the guise of freedom of religion... Marriage is a religious rite, not a civil right...
"We have the right to regulate practice, not belief." (Reynolds)
I think the Church has given that up as a political fight which could not be won; and concluded that for the non-religious, civil marriage was better than "nothing."
(I am not well-versed in this historic aspect, so somebody correct me if I'm wrong here.)
In some European and South American countries, rather than having the priest, minister, or rabbi act as a licensed witness for the state, they instead have two different marriages in two different places, one civil and another religious. I wonder if this isn't better, disentangling civil from religious marriage, inasmuch as the definitions of each are becoming more and more divergent.