IMO culture clashes would make sense if there were more fundamental differences shown in-game but in Bannerlord every culture is essentially classical-era Macedon with a different set of medieval weapons and aesthetics. There are many cultural sticking points besides religion, such as language (duh), views on revenge/forgiveness, preferred methods of land-use (i.e. Farmers vs herders), clannishness vs. attempts at meritocracy &c.Cultural stuff is not at all irrelevant in modern times. To a certain degree is is much more prevalent than in medieval or early modern times. Especially nationalistic feelings were not that present in the medieval times. There was of course the faith to divide the people and make them cruel and dump fanatics.
What you wrote about the fate of heretics is however more a development of the high and late medieval period. The retribution became stronger after the "crusades" against the cathars, and new logic systems (partly connected to the thoughts of Thomas of Aquin) and the struggle between state and church influenced it. There are very seldomly reports about prosecution of witches before the 12th c. AD, for example, as the connection between magic (the early church denied the existence of magic) and the devil was a later invention. The Spanish Inquisition f.e. came into full existence only in the late 15th c. AD. It's interesting that it did not care much about witches (the focus of many othe inquisitions) but prosecuted more heretical people (or what they took for), homosexuals and moriscos.
We don't know about anything similar in Calradia, and it seems that such cultural differences don't play a role for mercenaries at least (or better: for nobody in daily military life). I think not-so-mixed armies are just more interesting from a gameplay perspective, lore or not.
Though my main source for how culture clashes work describes the 17th century and later so I'm not sure how much of it can be applied to the high middle ages.
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