I still fail to see how it's any different than any other moral disagreement. eg. If I were a evangelical christian, and he supported abortion rights for women, I can claim that he's literally trying to kill babies.
Right to happiness is not a moral question that needs to be debated every time someone on Fox News needs to generate mass hysteria for profit. I think the average person can differentiate between what’s moral and what’s immoral and where are the boundaries between the two. The USA is in a complete meltdown because some still insist on staying blind.
But you're describing what a large subset of evangelicals actually do, so that doesn't really help your point.