I just saw now that there is a continuous eastern head of nestorian christianism, with no land but 2 vassals. Jewish religious heads could work in the same way, as a hereditary exiled nasir title, that after certain events asks for a holding in a province in Iraq or Andalus similar to how holy orders asks the king of Jerusalem after the crusades, and that improve the general state learning.
Khazars and ethiopians are problematic because it's very hard to represent an african minority with sparse historical knowledge about them or a jewish steppe nomad elite; in both cases the civilization and the culture weren't jewish. And the opposite of what someone said: khazars didn't convert anyone to judaism, they were actually converted by jews already settled there in the caucasus and the black sea, who fled repression in the byzantine empire, sassanid Persia- where they were very influential- after the muslim invasion, the persian client jewish state after byzantine invasion of Palestine and even after the bar kochba revolt. There was a very strong continuous presence of jewish merchants in the black sea.
Judaism could be modeled in many ways: people wouldn't convert to it only by being educated by a courtier, they could gain piety with learning and learning related things, and they wouldn't be able to rule any holdings besides cities inside republics and their own religious bulding. Religious holy sites could be maybe Jerusalem, Safed, Tiberias, Cordoba and/or Bagdah.
All in all I agree with everyone else, judaism should be implemented in a religion DLC, i.e. theocracies.
Sorry, I should have been more clear, I was praising your criticisms of their posts, the i.e. was an example of their repeated posts, not yours.
Apologies, again.
Oh, I'm sorry for wrongly interpreting your words.