Superficially, Barbarians seems like walking avatars of Anarchy; beholden to no one, chained to nothing. But this is an impression of people who don’t live in a barbarian society, with its petty tyranny by the chieftains, the occasional culture of slavery, the low-level constant warfare with other Barbarian tribes (and just about everyone else), etc. Barbarians live within hierarchy, even if it is more rough-and-ready than ‘civilized‘ hierarchy.
Perhaps ironically, Barbarians that come into contact with ‘civilization’, and the Anarchists therein, are the most likely to become Anarchists themselves, rather than those in the wilderness. While most Barbarian archetypes are suitable for Anarchist Barbarians, the Urban Barbarian archetype is especially complementary.