Hearts of Iron 4, Vic 2, Imperator Rome, EU4, ETC

Yeah, the part about the historical separation is definitely true. As for crusades, i think their impact on the game is really pretty minimal. I've always thought the name of the series doesn't really fit with what you actually end up playing most of the time. I mean you can play entire campaigns without ever really having to interact with an actual Crusade crusade depending on where and when you start.

Plus, crusades aren't even really that special because any at least somewhat militant faith gets its own version of holy wars, so in a way it's equal opportunity problematic (though that in itself could be criticized as a form of propaganda by projection, because in reality most of the rest of the world did NOT have their own version of the crusades).

I would say the most problematic aspect of CK is that by its very nature it puts aristocratic elites ("noble" families) in the driver's seat of history. It implicitly adopts a "great man theory" view on (pseudo-)history, and does it more so than any other Paradox grand strategy title. And that's not really fixable, it's built into the DNA of the game, as its whole gimmick is that it's character/roleplay driven.

You just have to be aware that what you're playing is closer to fantasy than actual history. That's probably also why it lends itself so well to fantasy mods.