What do you define "reality" as? Government? Culture? Military? Religion? History?

Crusader Kings is a simulation game, and the point of a simulation game is to simulate history as you would like it to be. So in that regard, Crusader Kings is not true to reality at all.

Also, both the Charlemagne start and the Old Gods start has Catholicism and Orthodox as two separate religions, when before 1044 they were still one religion.

There are a number of other simplifications, as well. Here I'll focus mainly on succession laws.

For example, Muslim rulers in CK2 use "Open" or "Turkish" succession, where the "strongest" son is the one who inherits. This is an abstraction of the Ottoman system of succession, where the first son to make it to the capital and declare himself Sultan would become Sultan (Ottoman law also required him to kill his brothers if possible), but as its name suggests, it was a characteristically Ottoman succession practice: it wasn't necessarily practiced elsewhere in the Muslim world.

For another example, Byzantine Emperors (the term there is rather anachronistic––in CK2+ the term "Basileia Rhomaion", or "Empire [of the] Romans", is used, which is closer to how citizens of the ERE referred to themselves) have access to the "Born in the Purple" trait, where sons born to a reigning Emperor have a higher claim to the throne than sons born before he took the throne. This, too, is an abstraction of the notion of "Porphyrogennetos", which was a title the Emperor would often claim in order to add extra legitimacy to his reign (specifically, a "Porphyrogennetos" had to be born in the "purple chamber" of the palace to a reigning Empress who had undergone a special ritual).

Succession debatably never reached the status of "law" in the ERE. Rather, Emperors would often appoint their favored heir as "co-Emperor", so that there would in principle be no succession crisis and so that the office of "Emperor" would not be vacant even for a second. (This is loosely modeled in CK2 via the "Despot" title, which can be granted to favored sons to move them up the line of succession.) Another way to get onto the throne was to marry the widowed Empress, which would never happen in CK2, where succession is almost always dynastic.

In fact the notion of a succession "law" as it's implemented in CK2 is generally too simple. For example, agnatic-cognatic primogeniture debatably didn't become "law" in England until the reign of Henry VIII: before that, the crown could pass to the firstborn son or to someone much better liked by the military or nobility, depending.

In a lot of other respects (keeping track of claims and pressing them, marrying family members off to form alliances, whatever), it's somewhat close to historically plausible. Overall, it's a game, so some level of simplification should be no surprise. History is wild and unpredictable, but a player needs to have some idea what to expect next.