This about as accurate a caricature as describing someone's position as "every one of my beliefs is true"

"such as" means that what follows is an example, not an exhaustive list, and what I said doesn't apply just to that example and to nothing else. If rationality means deriving conclusions logically from premises, then I concede that opposition to gay marriage can be rational, given appropriate premises.

Why are you so convinced that is in fact a true belief since you don't seem able to produce any argument for it?

It's pointless to produce an argument for it. The chance that even with a valid argument I could persuade someone who opposes gay marriage, to support gay marriage, is negligible.