but it still seems wrong for the state to even be involved

Well, then... how about a system of marriage where the participants can choose either state or church marriage or both, depending on their beliefs.

Choose church only marriage, and you are married forever in the eyes of God, but you forfeit all protections offered by our civil and legal systems. No familial health benefits; no community property nor child custody rights should the marriage fail.

Choose state only marriage, you get all the state protections and benefits, but at the risk of (depending on your belief system) death everlasting at the end of your corporeal existance or even burning in hell because you lived in sin with your partner.

Choose both, and get the best of both worlds.

Whose interests would be damaged by such a system?

tanstaafl.