The conservatives bedeviling our society do not have wrong ideas. They do not disagree with you. They are not influenced by logic or fact. They live in a world of fearful emotion. When confronted by these contradictions, their huge amygdalas perceive contradictions with normal expectations and cause them to have alarming ideation and fight or flight hormones are secreted.
When you hear a weird noise at night and have a feeling of dread, that's your amygdala speaking. You have no facts to support dread. You live in a world with no zombies or serial killers. Still, your amygdala generates the worst possible ideas and emotions.
Because your amygdala is the right size, the rest of your brain (something called the 'anterior cingulate cortex' is responsible for dealing with complications like a weird noise or ideas that don't fit your previous expectations) quickly dominates your thinking with rational explanations, essentially generating a new faith system based on its rationalization of the event.
For amygdala people, the fear doesn't go away. The mental process that rationalizes is weak and cannot secrete enough hormones and neurotransmitters to compete with the alarm.
The only thing that calms is faith. Ideas with their intrinsic back and forth of conflicting thoughts always stimulate fear. Only the certainty of faith, of previously known and accepted ideas, avoids stimulating the amygdala and reduces the alarm.
For these people, gay marriage (abortion, black people, etc) are like weird sounds in the night. These things violate their expectations and their amygdalas react with alarming ideation.
Opposing these people with facts and argument does nothing. Pointing out biblical contradictions simply stimulate these overgrown amygdalas to more alarming ideas, to more fear.
I haven't figured out the way to communicate to the People of the Amygdala but, it's not with facts. We need to find a way to talk to their fear in a way that subverts and lessens it. We need a way to introduce new articles of faith without stimulating the gigantic amygdala.
Tough goal but, it's the only way we will survive as a society.
Update 11/29/18: Researchers examined the role of fear and security. Slightly different angle. Consistent. Very interesting. Washington Post