In all honesty, that would help a little, but the religious lore is still spotty at best and poorly written. The fact that people had this 'mere misunderstanding', despite your insistence that the fact that some people do get the point justifies it somehow, is indicative that it needs to be written more clearly, but also, the tribunals existence as an authority at all is not really detailed. The impracticality to write a holy book about a fictional religion doesn't really justify a spotty religion, nobody is asking for a holy book, they just want the central theme of an entire faction and set of characters to be something slightly more than "we're religious because, uh, religious", because inevitably without something more than that literally any chaplain of that religion will struggle to play a believeable chaplain. Even if other factions share some of the lack of depth, 1) that doesn't justify lack of depth thats just shifting blame and 2) they are doing something right as they haven't produced as much controversy, I attribute it to the fact that most of them are pagan faiths that don't *need* the justification because they aren't widespread anyways. I agree that a more cultural basis for the religion would help, but it won't do much to reinforce its influence on Dominian characters' day to day lives if the only listed motivation for its cultural inclusion is "its tradition". The themes are also clashing, as there has been word saying that they're not a theocracy, the religion is just a tool used to control the masses, but that doesn't add up. If your religion is where your authority over common people originates from, then they are likely to be able to strip you of authority (as with popes naming kings and excommunicating them), but if the ruler has so much power that this doesn't matter, why does he even need the religion? as a pragmatic ruler, why does he not do what the soviets did and strip it entirely? I get the traditionalism and that there is still potentially a place for the religion within an authoritarian regime, but as was mentioned before, backing these laws with death makes them only as effective as secular laws.
TL;DR, writing the lore more clearly is entirely necessary, nobody is asking for a holy book, but the religion should be detailed and strongly written enough that chaplains have something other than "obey me or else is my religion" and "when u die u go to heaven" to work with (dont care if "other factions" are just as bad, those are pagans its okay), and the themes of "authoritarian fascist state" and "authoritarian theocratic state" should be combed through for inconsistancies