"Therefore, in our roles as Christian ministers, we, the undersigned, commit ourselves to disengaging civil and Christian marriage in the performance of our pastoral duties. We will no longer serve as agents of the state in marriage. We will no longer sign government-provided marriage certificates. We will ask couples to seek civil marriage separately from their church-related vows and blessings. We will preside only at those weddings that seek to establish a Christian marriage in accord with the principles articulated and lived out from the beginning of the Church’s life."
In other words, couples will have to go to a judge to be legally married, and then head for the church for "vows and blessings." (Which is exactly what some European countries have done for decades). For a Christian, the "real" marriage IS the vows and blessings in church.
I can imagine young couple expressing this view by thumbing their noses at the "legal" marriage, showing up in a judge's chambers in old jeans and T-shirts, and minus any rings or family members. (Their T-shirts might read: "This is not a REAL marriage ceremony!" or: "God designed marriage, not the state!") And then they would go on to the church and dress up for the "real" wedding, performed by an agent of God before friends and family, complete with rings, a big cake, and all the trimmings.
Or maybe not: Not everyone is as aggressively in-your-face as I am . . .
Another solution is a destination wedding—flying the entire wedding party, including the minister, to some pleasant country that upholds genuine marriage. It would be good to bring tourist dollars to countries that do this. And to let them know why you've come.
In my opinion, Chuck would have been proud of these ministers.