Marriage is a religious rite, not a civil right.
OK at this point I’m still not sure what you’re talking about. In terms of moral theory and history, you can argue that marriage is a religious institution and right. Legally, the right to marry, and the incidents of marriage - as practiced and actually enforced by the States - is not essentially religious. On the federal level, there is Supreme Court precedent from early in the last century dealing with a fundamental right to marry, and that right is not defined as essentially religious.
None of the above means there’s a federal constitutional right to gay marriage (or says that there’s isn’t one, for that matter.) That particular fight centers on the proper interpretation of the Equal Protection Clause of the 14th Amendment (and the Due Process Clause).
And now I go to sleep.