..and Paul is wrong. As long as there are legal issues tied to it, such as inheritance, property ownership, taxes, etc and as long as it is a legally binding contract, the government has the responsibility under the Constitution to ensure that there are clear legal definitions and the law is equally applied (Article 1 Section 8 'Weights and Measures' clause per the Federalist papers, Measures includes uniform definitions that pertain to legal matters. Also 14th Amendment, the equal protection clause).
In order for government to be out of it, it would immediately require that all existing legal contracts that pertain to it be either voided or changed (a boom for lawyers). All pending or recently passed litigation in relation to marriage issues (such as divorce property issues) would/could be challenged.
You then have the one hundred million or so married couples who no longer have legal contracts recognized and you run into another Constitutional issue regarding Ex Post Facto laws.
Marriages were not licenced in the US until Jim Crow, and it wasn’t an issue at all.
The whole concept of licencing marriage was to prevent “mixed” marriages.