Essentially, the theology is against the Jews, and it's a reverse mirror of the OTL First Crusade. A strong Byzantine Empire gets in over it's head against the Arabs and Khazars and appeals to the Rome-loving Otto III, rather then the weak (but with a strong ruler) Byzantines calling upon the somewhat apathetic Western rulers.
And rather then desiring to take the Holy City, the Crusaders want to take the rich cities along the Khazar trade routes. At this point, the Khazars are extremely rich.
Part of the problem is that this is not at all a mirror of the First Crusade. The First Crusade was entirely about moving to the Holy Land to liberate it from the infidel and permit free travel to the sacred sites. Rich cities had nothing to do with it. Wealth had nothing to do with it -- I'm not talking of individuals here, but of the mass movement.
And they weren't so much driven by secular rulers as by the clergy. To get a good early crusading theme down you need a combination of factors -- a reforming drive in the Church, a popularity of pilgrimages, and a goal. The goal was not to kill infidels (though that was certainly not discouraged, and might be considered a fringe benefit), nor to win lands (the majority of the Crusaders went home, and that was the great weakness of the Crusader states ever after). It was to go to the holy places - something difficult and dangerous to do since the Seljuks started killing pilgrims for sport.
So to get a mass movement like OTL crusades, you need the social and theological factors which combined. Otherwise, it's a just another war, with some cheap rhetoric tacked on as an afterthought. Sort of like Karl's Saxon expeditions.
Remember when writing that no one is a villain in their own eyes -- hating folks is pretty common historically, but no one ever went anywhere or did anything meaningful on hate alone. Even Nazis had a vision of the future that involved what they saw as positive movement towards a desired goal.