'Judaism' is for an occasional random lowborn courtier who pops up in feudal courts. He can't be given land, can't marry a non-Jew, and can only be given the council posts of chancellor, steward and spymaster. As such, he can't have the 'martial' or 'theologian' education traits; to compensate perhaps give a bonus to the chance of getting a better version of the traits he can get, to represent better Jewish education. (That would be more elegant than giving Jews a bonus to tax income or the like.)
Good points, all. Though I disagree about the partioning of the religion into Khazar Jews and non-Khazars, which I'll get more into. As for historical contact between Jews in Muslim lands and Khazars:
http://en.wikipedia.org/wiki/Khazar_Correspondence
Then, you have 'Khazar Judaism', a pagan religion. That way you don't have Khazar nobles intermarrying with Sephardic Jews and claiming counties all over the map, which you inevitably would if it was the same religion.
If the argument for dividing them into two seperate religions for game mechanic purposes is to prevent getting county claims all over the place, maybe a rule for Christian and Muslim rulers that prevents courtiers in their realm from passing on titles to Jewish (religion) courtiers? Not that it would make a whole lot of difference, if that wasn't implemented I think. My experience whenever the AI has one of their counties or duchies pass on to someone outside the realm faith, the count/duke/king is either asked to convert which he does, or his vassals rise up en masse against him.
Instead of a two seperate religions, perhaps include a special trait for "Court Jews", called....well, "Court Jew" (or something abit more refined). The trait would prevent the "court Jew" from owning or inheriting any title claims.
If he the court Jew is succesfully invited into a Jewish realm's court, he automatically loses that trait, and can once again be allowed to own and inherit title claims. If a female claimholder is taken as a concubine, any claims pass on to closest relative in a Jewish court when she's made a concubine and thereby "Court Jew".