Perhaps the Khazar Khanate has a more complete conversion to Judaism? From the late 800's on, you get a great number of Jewish merchants, missionaries, etc. coming to the nascent Principality of 'Rus, giving them a leg up on the Muslims and Christians...hmm. How big were the early Russians on pork?
Borders wars existed OTL between the Poles and their Orthodox neighbors to the east, and I don't see this being particularly worse or better in the pre-Crusades era: it's not like they're going to get much help from the Germans or the French. I dunno how much their cultural isolation is going to hurt them in the first couple centuries - what did Russian "military tech" look like 1000 AD compared to it's neighbors? How much had it advanced by the 1200's?
Assuming we haven't butterflied away the Mongol invasions, Russia should look rather ripe for crusading Teutonic Knights and Poles after the 1240's (and then there's those pesky Lithuanians. What odds they convert to Judaism early in this TL to get allies against the Baltic crusade?). It's hard to say how well they'll do - again, I'm not sure how much their cultural isolation from both the Christian and Muslim worlds will retard their military skills compared to OTL. (I'll note that OTL, the Russians being "fellow Christians" didn't prevent the Knights from trying to take Novgorod. Indeed, will they crusade against Jewish Russia that much more energetically than against "heretical" Russia? The Ottoman empire OTL got along even worse with Shi'as than it did with Christians.)
Jewish legal and political influences: will a Russia under a Jewish monarch undergo the sort of devolution that it did OTL? Is there anything in medieval Jewish law and tradition that might push for primogeniture? (And we haven't even considered what a more solidly Jewish Kazhar state might come up with in terms of modifications of Jewish tradition, being an established state with needs rather different than a Diaspora. Quite possibly the Judaism of "Jewish Russia" is different enough that the Jews of Europe condemn it as heresy.)
BTW, Russia wasn't that "big" a country until recent times - geographically extensive, yes, but very thinly populated. Historical estimates are that the population of European Russia (including the Ukraine) didn't surpass France until the 18th century.
If Russia survives the 13th and 14th centuries to reemerge as a united kingdom, it may not be that different from OTL: a terribly backward and isolated state, looked upon perhaps like Safavid Persia - a useful ally against the Turk. (Thought: Russia reunified not by Moscow, but by a Jewish Lithuanian dynasty?) Whether it can ever overcome the severe cultural barriers to modernizing with European help as Russia did OTL, that's another question. (Although it's hard to see a Jewish Priest-King looking back to the glories of Solomonic Israel doing a Peter the Great in the shipyards of Amsterdam, Peter was hardly the model of a Byzantine emperor himself).
All rather improbable, perhaps. But I will admit to being tickled pink by a mental image of King Peter III of Russia leading an invasion of the Ottoman empire in the 1850's to liberate Jerusalem and rebuild the temple...
Bruce