You're confusing two disparate issues.
Issue one is can gays get married by a religious institution. The answer to that question is already yes and always has been yes. Government does not stop anyone from having a marriage ceremony or just claiming to be married, because getting married in the religious sense is merely a non-binding agreement between two people that may or may not have been witnessed. Well non-binding unless the state you are in has common-law marriage.
The second issue is the one of the legal matter for the civil union of two people who have agreed to enter a marriage contract, aka. marriage licence.
Legal marriage definition:
The legal union of a couple as spouses. The basic elements of a marriage are: (1) the parties' legal ability to marry each other, (2) mutual consent of the parties, and (3) a marriage contract as required by law.
Marriage | Wex Legal Dictionary / Encyclopedia | LII / Legal Information Institute
I know they use the term contract, but as I pointed out it's bogus.
A contract between two parties is something they work out between each other. If you do this, I will do that. If I quit my job and raise your kids and you leave me for your secretary you bastard I want half your shit.
A contract is not something that government defines, implements and changes at it's own whim. That is just a government program.
Arguing with a libertarian that life is unbearable because someone wants things from government and government is being oppressive because they don't give it to them isn't going to ever get you anywhere. While as a Republican you may still want government, and lots of it, I would think that would bother you less than what liberals want.
You are still not listening. Without governance of some kind, there is no means to enforce and/or arbitrate a contract between two or more individuals. Without some means to enforce contracts you could only rely on a man's word as his bond. The paper of a contract would be worthless without a body to provide enforcement.
Having a body that enforces contracts without having to have people self enforce agreements is one of the corner stones of civilization since we left the trees.
I support having civil courts to enforce contracts, is that what you mean? That isn't what government marriage is, but yes, I believe contracts should be legally enforcible.
I support having government police, military, civil and criminal courts, roads, management of limited resources and recognition of property rights. Those are things that expand my liberty rather than contracting them, and they are not doable without government. Everyone has to buy in, you can't have criminal or civil courts recognized by some and not others. You cannot have different bodies recognizing land ownership. I see no solution to those things but government.
I am also saying that government marriage is not a real contract. And I've explained why that is so. It's a government program. And rather than expanding liberty, government uses it to discriminate between citizens and redistribute wealth.