I would argue that banning gay marriage is not a right nor a civil right so to speak. The arguments against gay marriage is made largely on religious grounds. Rarely are secular arguments made against gay marriage. There is no valid biological or scientific reasoning for its prohibition. Therefore the burden of proof is on those that want it prohibited and they have no rational real-world proof to support their beliefs.

The 1st Amendment explicitly prohibits law from being created based on religious beliefs. They can only argue on secular grounds and then that can be deconstructed using the Equal Protection Clause. Therefore while one can hold a personal belief against gay marriage the state has no right to prohibit gay marriage.