The issue is really that left and right as politial stances are not based on a stable framework, and everyone can place every political system into either categ

The issue is really that left and right as politial stances are not based on a stable framework, and everyone can place every political system into either category if they really want to (as often happens when people claim the nazis were left wing because they used the word "socialism"). What's actually important is that none of the above fit well within contemporary US-centric understandings of "left" and "right". I say US-centric because some people center-left in the US would be considered center-right where I live - this is how fragile this dicotomy is.