That would be a violation, because it would be violating the 1st Amendment, which explicitly says no messing around with religion (we don't have religious tests, ,etc). There is no amendment that says "no defining marriage in ways that don't reflect sexual preference. However, if, for example, California were to pass a law stating that you could only marry someone within 2 years of your age (my wife is 4 years younger than me), then I would simply refuse to move there. Hooray for freedom of choice .If california decided to ban christians from being allowed to marry, while everyone else could, would you still champion the "whatever the people want, they get" philosophy? Or would you cry out for equality?
What I wouldn't do is invent a positive right to a marriage certificate. Rights are negative things, not positive things.
And you believe in positive rights, such as to a marriage license? You're a crappy libertarian .That's the difference between a republic and a democracy. In a republic 51% does not get to vote away the rights of the other 49%.