The idiocy goes right over their heads
I don't know if conservatism is really about preferring older solutions. I think that's the marketing. It's pithy but I think the "conservatism means there must be in-groups the law protects but does not bind, and out-groups the law binds but not protect" is very explanatory. That might not be what they tell you, but humans generally feel a thing and then reach for a socially acceptable explanation afterwards. But it's really just "I want my group to thrive, and the other groups to go away". That was probably a survival trait in pre-history. Now it's just being an asshole.
One of the problems is that the way these people are dividing people into groups is kind of stupid and self destructive. Instead of seeing "all of us who trade labor for money have common cause", they think they're in the same tribe as the ultra wealthy. Instead of recognizing that that queer couple is struggling to pay bills and raise their kids, they mentally put themselves in the same group as some rich assholes who (under)pay a nanny to raise their kids and never spend time with them. They vote to cut social programs because they think it'll hurt their out-group, but it's hurting them. They have the groups wrong.
I think there's also more fragility among conservatives. They hear something like "white people perpetuated the horrors of slavery" and their ego freaks out. That's an attack on the in-group! Can't have that! And so they reject it, because the in-group is the most important thing.
To be conservative is to be a failure. To be less decent. It's not hopeless. People can change. But I don't think "Oh, they just prefer older institutions" is apt. It's about dividing people into us-and-them, and really putting the hurt on "them".