We have pseudo-state-religions in Terran now. Sanguis Astroism and Triunism hold special legal privileges, and other religions have slightly restricted access.
Nobody in Terran is hyper-critical of Sanguis Astroism, or at least not public. I have nothing against SA. I don't want a modern Republic.
It's worth noting that ancient Greek republics had a state religion. I seem to recall Socrates drinking hemlock after being convicted of charges which included theological deviations of various kinds.
Then obviously Greek Republics are not "real" republics, as defined by the resident expert of political systems, Glaumring.
