I think fear explains a lot of differences.
Two are rational criteria to make moral judgements (harm and fairness) and the other three are emotional irrational criteria.
Humans are only partially evolved when it comes to morality.
I think the other 3 (Purity, Authority, Ingroup) evolved for good reason in us as humans, and exist in some extent in all of us (even in the very liberal people as seen in that graph). Having strong ingroup identity and authoritarian thinking does make for a more socially cohesive ingroup. It is why conservatives are so much easier to organize than liberals. Organizing liberals is like herding cats, yes? Strong ingroup identity also has been shown to mean kinder behaviour to those within your group (and meaner behaviour towards those outside of it). Tribalism is the flipside of empathy to a large extent.
Purity I think evolved as our "yuck!" reflex, first to environmental dangers, and then extended to the social and psychological. I don't see any value in it today. I wonder how conservatives would explain why it matters, without pointing towards religion.
Can any conservatives here comment on that? Why does "purity" matter to a conservative atheist? Or does it?