I grew up in eastern Kentucky and I think I have some insight on this.

In his mind, it's coming from a deep feeling of insignificance. It's cultural in Appalachia. It was the original abandoned inner city ghetto of this country. In the early days of expansion, people with ambition and less blind stubbornness moved on when more of the frontier opened up. The people that are there are the descendants of the people who were too stubborn to leave. The outside world said fine, stay there, and forgot about Appalachia completely. In turn, this became the cultural identity of the place. The people have internalized the lack of worth that the outside world sees in them. They have no drive, ambition, or reason to believe anyone outside of their immediate community and Jesus give a shit about them. The only pride they have is in their stubbornness, and in the identity that chokes all of the life out of them. When a stranger shows up wanting to help, the first thing an Appalachian thinks is "what's the catch?" Because they do not feel they are worthy. When they hear praise, they immediately question its motives. They fight with each other over who can be the least. Drugs and addiction have made this worse, because addiction is a shame factory.

This man doesn't see why his prejudices matter to anyone because he sees himself as insignificant. He doesn't even see himself as prejudiced because he is submitting his will on the matter to the only thing he has to believe in. I imagine his inner dialogue goes something like this: What does it matter if two men get married in Rowan County? I don't begrudge them, there are plenty of places for them to get married, just let me go be nothing again, like I deserve.

His prejudices themselves are not just simple religion-based bigotry. Feeling pride is shameful in Appalachia. House of Cards nailed this in S1 when Frank visited his constituents in South Carolina and said about them, "my people are a noble people. Humility is their form of pride." Two men being proud enough to walk into their courthouse and want a marriage license when they feel it's morally wrong is the straw that breaks the camel's back. They don't see any shame in two men loving each other, they are judging them for being proud of it in their face. That's why he doesn't think of it as hate.