One day I'll actually do the research to make a "what if the Khazars actually did convert to Judaism, and then survive to supplant the Russians?" AT reasonable, and it will result in this.
- Khazar Khagnate elite becomes Jewish to remain independent of Christian Byzantines and Islamic Caliphates
- Khazars defeat Varangian Rus in Kiev, entrench further culturally, are not supplanted, survive in some form until the Mongol conquest
- Golden Horde Judaizes instead of Islamizes
- When Mongol state power collapses, the Judeo-Turkic entity in Kiev (Golden Horde) expands following the same geopolitical logic as the Russian state, but with extreme political interest in the Levant
- Potential attempts with the Ilkahanate or equivalent to consolidate Anatolia and conquer the Byzantines
- Fierce violence against the Mamluks over Jerusalem in the post-Mongol-collapse world (the success or failure depending on whether the Golden Horde or the Ilkahanate takes Constantinople in the previous step)
- Instead of a rivalry with whichever Islamized Turkic successor to the Ilkahanate ends up being (and eventually whichever Islamic Turkic entity survives in Anatolia), they are friends.