There was very little hinted about it so far:
Apparently if your current ethics don't quite get the job done, and pops are unhappy, the opposite ethics become more attractive.
Xeno tensions could move some towards Xenophobia, and atrocities towards them would lead to Xenophilia. Also suffering large military losses, or waging an excessively drawn-out war would cause pacifist tendencies, because war looks like a bad idea. If your nation is in "peril", there will be more militarist attraction.
So far, "Poverty", maybe from few consumer goods, as well as "not feeling safe" from high planet unrest, seems to lead to Authoritarian, a lack of freedoms and doing purges seems to lead to Egalitarian.
The ethics of other nations, and your diplomatic relation towards them will also influence them, allies thinking alike, and rivals ethically diverging from each other.
Also I suspect there will be periodic events that would shake your country's belief in a certain ethic. Some badly handled AI malfunction event would make them doubt materialism, for example.
EDIT: Let's not forget the strongest means to control this kind of thing: Helping the ethic factions out, making them more or less attractive through the use of influence. Although, for the faction to exist, some pops must have the suitable ethic.
