I’m going to divide my response into a political answer and a philosophical/religious answer.
Political
Most understand: Death penalty. I completely get the desire to kill the absolutely worst criminals, especially the ones who hurt children. I understand the emotion completely and my opposition to the DP is based on concerns about inherent error in how it’s administered not because I think some people don’t deserve it.
Least understand: Opposition to gay marriage. I’ve never heard an answer that isn’t rooted in either overt homophobia, covert homophobia or some sort of legalistic tautology (gay people can’t get married because “marriage is between a man and a woman.”) I really don’t understand why anybody thinks they would be harmed by it.
Philosophical/Religious
Most understand: Belief in God. Not necessarily belief in miracles but I totally understand that subjective personal experiences can be convincing and real and that a life of faith can seem so innate and organic that you can’t conceive of not believing in god any more than you could conceive of not loving your children.
Least understand: Young Earth Creationism. It seems to me that a sincere belief in this stuff requires such a level of denial and flies so in the face of suffocating contrary evidence that I sometimes wonder if anyone REALLY believes it deep down or if they’re just putting on an act. Listening to somebody defend YEC is like listening to them defend a belief in the Easter Bunny. I feel lile they must be whooshing me.