ehh I don't know, might be able to make the argument that this is people voting in a law favoring certain religious beliefs to "irreligious beliefs" which is tied to the 14th amendment (see Gitlow v. New York and Board of Education of Kiryas Joel Village School District v. Grumet) but I tend to think Davidson Deac II is correct in that 14th is where this is most likely to get traction in unconstitutionality.
If it comes to the Supreme Court, some on the far left of the court might cite the 1st amendment, and religious beliefs, but for the rest of them, I think the 14th will be the centerpiece of their argument should laws against gay marriage be overturned.
Of couse, the whole thing would go away if governments get out of the business of issuing marriage licenses, and make it a purely religious function. And they should, (but they wont).






