There are some hilarious misconceptions that members of those factions have about their own ideologies. Far-left is against the police brutality, but there is a 100 year history of perfect correlation between leftist regimes and policy brutality.
Far-right is against government interventions in all economic matters, but that also has never materialized anywhere else.
The bottom line is that anything that's far-something requires suppression of the society's natural tendency to return to the center.