Both your personas are oddly constructed and not really representative of a political quadrant with state-individual empowerment on the vertical access and state backed private property on the horizontal.

Free speech, reduction of private property, dissolution of centralized state and wealth redistribution are all very classic bottom left (anarchist) principles for instance.

I would think anyone below the center line vertically (so anarchists to free market libertarians) would support what you call “cancel culture” since is a powerful form of direct action.