Nonsense. Grandfather any existing marriage, issue a certified cohabitation certificate or whatever you want to call it form now on. Remove MARRIAGE to the church where it started and belongs.
So you want your marriage to be legal, to be “grandfathered” in.
You then say that you want others to not get a license if they seek to make their marriage legal, but instead to get a “certified cohabitation certificate”.
So a marriage is still either legal, or not legal.
As far as marriage being purely religious, no it isn’t, for many, it has nothing to do with the mosque, or church.
Nobody required you to seek to make your marriage recognized by the state, the United States has never that requirement, individuals seek it out on their own. Millions of Americans have not sought legal status for their marriage or relationship, over the centuries.