It is the government that has made marriage a factor of life and it is the government that should determine the implementation. The government should take religion out of the business of marriage by requiring all ceremonies to be performed by a approved government official. Anyone that wishes to receive the benefits and rights of marriage recognized by the government would need to have a civil marriage and only a civil marriage would be recognized. A religious marriage would not be. Religious ceremonies can still be performed but would not be recognized by the government.
It is the government that decides the age that couples need to be. It is the government that decides what medical tests they need. It is the government that documents the event. It is the government that documents when they are divorced or anything that is the result of the marriage.
The only thing that religion should be allowed to do is within their own walls that pertains to the practice of religion. They don't get to violate building codes when they build a church or a school for their kids. They don't get to avoid paying any fees for the use of any government facility.
Marriages was not something that was considered necessary during the first 100 years or so in the US. Many would just live together until one tired of the other. Usually it was the man that left. That was one of the factors that resulted in marriage being implemented by the government. They were considering the impact on the community supporting abandoned women and children.
Probably as late as the early 1900's marriages weren't always recorded by the government in the US.
Just as the states has an interest in marriages the federal government does too and probably more so.