It is my opnion that government should not be involved in marriage at at. There should be no marriage license. If government wasn’t involved in granting permission to get married (license) the homo/straight “marriage” dispute would not and could not exist.
Well, just thinking out loud here - if they aren't involved in marriage at the beginning, they'll still be involved in marriage at the end. Even if you were to advocate that the marriage contract would be unrecognized in government, for purposes of taxes and such (which would be a bad, bad idea), the courts would still get dragged into it when one of these marriages end, either due to death or divorce.
It seems that it would be impossible to completely remove government from marriage, and I'm not sure it would be a good idea even if it was a possibility.
They would find something else.