Good question GT.
Haidt admits that as a liberal he too equated hierarchy = power = exploitation = evil.
He was later influenced by the work of Alan Fiske who described the "Authority Ranking" social relationship. Drawing on his own work in Africa Fiske showed that people who relate to each other in this way have mutual expectations that are more like those of a parent and child than those of a dictator and fearful underlings.
Conservatives react negatively to anything that subverts the traditions, institutions or values that provide stability.
The liberty/oppression intuition is interesting. It was a late addition to Haidt's scheme. It arose out of the need to control oppressive hierarchies. Once we invented spears and the language skills to gossip about bad leaders no tyrant was safe. We see it today in the right's demand for small government and Tea Parties slogan "Don't Tread on Me". Conservatives are more parochial. For them the sacred value is liberty.
But exactly the same moral intuition is motivating the left's drive for social justice and opposition to capitalism. Liberals are more universal in their moral concerns. Hatred of of oppression is found on both sides of the political spectrum. For liberals who rely more heavily on the care/harm foundation the Liberty/Oppression foundation is employed in the service of underdogs everywhere. It leads to appeals not just for equality of opportunity but equality of outcome.