"In particular, when it comes to marriage, outside of the aforementioned libertarian fringe, there is a total and unanimous agreement that marriage is not a contract whose terms can be set freely, but rather an institution that is entered voluntarily, but whose terms are dictated (and can be changed at any subsequent time) by the state."

If true, this is a new thing. In the past the terms were dictated by the church. I doubt you will find unanimous agreement today that the views of the church are irrelevant to marriage. So perhaps the total and unanimous agreement is something not quite so total, that can change more than this implies.

"Therefore, when I hear a libertarian argument applied to marriage, I conclude that there are only two possibilities:"

This seems to be a failure of imagination. How about number 3: they are an honest libertarian who thinks that a marriage contract should be a contract like any other, AND that there are certain rights that are not alienable through contract.