That falls back to the whole separation of church and state argument. The far left is know for wanting this except in the case of "Marriage".
Obviously, it doesn't. As religion doesn't define marriage under the law. No one gives a fiddler's **** what religion has to say on marriage under the law. Not the law. And certainly not the courts.
There's your separation of church and State.
The government should not be in the business of "Marriage" anyway.
Says who? There are all sorts of legal rights and privileges that the State protects with marriage. Inherentence, Work benefits, medical decisions, social security benefits, exemptions from testifying in court, child custody issues, joint property, etc..
If you want a marriage without state recognition, you can have one. Just don't file a marriage license and 'call' yourself married.
If however, you want a marriage recognized and protected by the State, you can have that too.
Its a win-win for everyone.