As long as the marriage contract has implications on tax laws, inheritance laws, property rights, child support, etc, then government does have a place to make sure the contractual terms are clearly defined and consistent. The Constitution authorizes Congress to set the standards of 'weights and measures'. According to the Federalist papers, legal definitions are considered a measure that is within the government's jurisdiction to define. If legal definitions don't mean anything or are inconsistent, then contracts and laws aren't enforceable.
If you want the government out of the marriage business, simply having private contracts between individuals, then all the laws and recognized contracts that apply to marriage first must be addressed.
I think if states just started opting out of calling what they sell marriage licenses and started calling them civil contracts instead, that would dampen the political fire connected with it.
Most clergymen will not celebrate a religious union (marriage) between anyone/thing but one man and one woman-defuse the politics that way-a civil union is simply a business contract, and religions don’t regulate those, whether they are between a man and woman, or any combination of participants.
I have tried to convey the very same thing on other threads but you put it in a much more succinct way.
As an aside, I am a bit surprised this poster hasn't had a visit from the kitties yet.