I like to think that libertarian and authoritarian are absolute opposites and absolutes.
Liberalism and Conservativism contain shades of each.
I think authoritarian is more a description of a political system rather than a political philosophy. Socialism, Communism, Nationalism, Despotism, etc. can all be authoritarian in how they are implemented. I believe libertarianism and socialism/communism are polar opposites in their views as to wheather public policy is a tool to advance the interest of the individual or the state.
Liberalism and Conservativism contain shades of each.
Yes. But how much of each depends on when and where you are talking about. In Communist China, a Conservative would be a hard core party loyalist - in favor of socialism and tight central control. A liberal would be in favor of more democracy and free markets.
I find it kind of oxymoronic that people who claim to be conservatives today can decry the socialism of FDR and his policies, yet champion the very government bureaucracies and programs they brought about.