This image got me thinking - shouldn't a faction generate a (small) amount of attraction towards it's chosen ethic, just by existing, to represent the faction actively going out campaigning, proselytising and generally trying to push it's agenda?
Otherwise if this event happened, you can just passively wait for the problem to go away because once that modifier is gone the pops affected should naturally drift away from authoritarian anyway. But if, as a result, of this event you end up with a small, self-sustaining population of authoritarian pops that would be a persistent problem unless you do something to deal with them.
As far as I understand it that's already the case and the larger/more influential a faction is the more attraction it creates towards its ethic.