Yet it feels wrong. Culture was not really an issue back in those days. What these events are supposed to model is essentially a conversion by sword. Of course it needs to be extremely costly to make the player consider other options, but it would be more appropriate to model this through the event itself (massive reductions in population and province income, increased revolt risk, several uprisings, -200 gold or so per province forcibly converted ). Also, the events should fire on a per province basis, to reflect the hypothetical Byzantine advance into Asia Minor. It would also be plausible to tie the trigger to the level of innovationness. A country has to be extremely narrowminded and fanatic to even consider mass expulsions for religious reasons.
Historically speaking you are right. Up to the 20th century it mattered more if someone had the right religion than the right nationality in Asia Minor.
However there is no other way to simulate that in the game - there simply is no gamemechanic within the game that allows a player to change the provinceculture of a province. That is only possible with events.
Simply imagine that the missionaries you send there are not simply preaching but bringing the orthodox equivalent of the Roman Holy Inquisition to those provinces when you send them to convert the province.
If you want to have it done differently take a look at the russian events to change their tatar provinces to russian. The russian player has to convert the provinces to orthodox FIRST and THEN they change the provinceculture.
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