God created marriage, but civil marriage was invented by man. With the French Revolution, religious marriage ceremonies were made secondary to civil marriage. This spread to other countries in the 19th century. Today, outside of the Middle East, civil marriage is the only legal marriage; religiously recognized marriage has no legal status.
With the rise of same-sex marriage, the tables are beginning to turn: civil marriage may not be recognized by some people if it lacks religious authorization. There is no question that the state has a right to recognize whatever marriages it wants for its own purposes. But the question is about what may be called social marriage. What does society recognize as a marriage?
Compare this with driving. The state issues driver’s licenses, which authorize people to drive on public roads. This license does not apply on private roads. For example, the owner or operator of a race track sets the standards for who may race, not the state.
Similarly, the state issues marriage licenses, which authorize people to be married for public purposes. When income taxes are filed, for example, those the state has authorized may file as a married couple. But what about when people enter private property? What about private purposes? That is a different matter.
Society, through religion, custom, and tradition determines who is married for social purposes, not the state. Whether by religious authorization or common-law marriage or whatever custom people follow, society determines who is married for social purposes. Society may follow the state — or not.