God damn I love The Righteous Mind. I'm only 55% into it and it keeps blowing my mind every page.
Regarding the morality module pie charts in your post.
I think a strong case could be made that the Liberty module actually is the most important since it is the one that allows all remaining slices of the pie chart to flourish.
For example, in a stateless society, people would have total religious freedom, there would be not christian lobby.. since there's nothing to lobby for! No zoning restrictions and so different communities with different values would arise. Sanctity module: check!

Without a state, everyone would thrive in a freed market. Satisfying the Care part of our minds since poverty would be pretty much abolished.

Closely tied to Fairness as well (especially in the proportionality aspect of it)
In a statist economy you have 2 ways to make money. Through competition, innovation, R&D, etc.

1. Through the political means: lobbying, bribes, etc.
   This makes the population very suspicious of rich people. "Who did he fuck over to get that BMW?"
   In a free market, after a few generations, people would realise that rich people are people that did something others needed. There would be but one way to make money. Through voluntary exchange. So the fairness part of our brain would be happy (:

I believe the same principles would apply to authority and loyalty since imposed rulers would be replaced by voluntary leaders

My 2¢ on the importance of the Liberty/Oppression module in 2016! It is ATM the most important