I wouldn't mind seeing Republic given a Good or Neutral Only tag, much in the same way Public Healers works. It seems to me that the evil civs (Infernal, Sheaim, Calabim, et cetera) would be far, far less likely to adopt Republic from the perspective of the civilizations and their leaders. On top of that, there could be diplo modifiers...maybe -4, +/- 2, and +4, ranging from Evil to Good, respectively, for a nation having a Republic, with various other modifiers for the other governments (for instance, Aristocracy, Theocracy, and God King might give a slight negative modifier, because of the authoritarian nature of those government types).
In this way, there's more "fuel" to make the AI more aggressive, and gives suitable reason for civs to try and stamp out Republican governments--if not only for the unhappiness they cause. It would also have the added benefit of making Republic a rarer government type amongst civs--at the least, you wouldn't see the Ashen Veil prancing around with it, and if the player really wanted it, it's only one religious conversion away.