If you want a Jewish Russia, you'll need an earlier POD. To borrow some ideas from what I've seen here on the subject before, perhaps the Khazar Kaganate survives for a far longer period of time than it did IOTL (no Sviatoslav, perhaps?), and a larger number of people within the Kaganate become Jews (in our world the extent of the conversion was probably limited to the governing elite). Spread by their traders, Judaism over time begins to spread northwards to the Rus...
There's one problem here. Opposition to Khazars was about the only thing tying Kievan Rus together. I don't see Khazars spreading their religion to Rus, frankly speaking... I was toying with "Jewish Rus" idea for some time, but couldn't find a plausible POD for conversion, barring ASBs or ISOT.
Now if you have a Jewish Russia (perhaps going in hand with a Jewish *Lithuania too?), chances are that it becomes the target for would be Crusaders coming from the west...
IOTL conversion of Rus did not cause conversion of Lithuania for 3-4 centuries more and if not for Mongols Lithuanians could remain pagans for some more time. Crusades are almost a given ITTL. Even IOTL a lot of Germanic activity along Baltic coast was within "crusades" framework.
The ruling dynasty that emerges would probably try to imagine themselves as the successors to the House of David, and would do their best to build their capital as the "New Jerusalem."
I think it wouldn't be too tough for newly Jewish Rurikids to find some bride from a Jewish family which could trace their lineage to David (even today several families can reportedly do that), so "Rurikids-Solomonids" are very distinct possibility. And "
New Jerusalem" lore had been adopted even IOTL. ITTL it would be founding myth.
It's no gurantee that Jewish *Russia would be some sort of superpower ruling over large swaths of Eurasia, but there are many directions that you could go in...
I'm of opinion that relatively modern (for the day and age) agricultural civilization controlling Kama and Middle Volga basins in 16th century would at very least get Western Siberia almost inevitably. And this is the area where "Great Pork Border" goes through Eurasia

So it is very possible that Jewish "Volga Principality" would end up controlling Urals and Western Siberia.
It would have rather large effects, but most importantly Russia will likely not be unified. While Ukraine, the South (European) Russia and South Belarus become Jewish, the north is unlikely to be willing to give up pork, which were one of the primary sources of protein there.
Yes, IOTL spread of Islam in Northern part of Volga basin had been stopped by this feature (at some point sheeps and goats cease to be viable substitutes for pork, I call it "Great Pork Border"). There are two possibilities here:
- Northbound spread of Judaism stops along Bryansk-Ryazan-Nizhni Novgorod line, with Northern Slavs remaining either Pagan or Catholic. Northbound spread of Slavs into OTL Central Russia would be likely fueled by religious dissidents, so expect *Vladimir duchy to be in close alliance with Novgorod and very hostile to Kievans.
- Cunning rabbis decide that "Rus is well worth a pig" and allow pork consumption (after all, swine does have cloven hoofs, it just doesn't chew cud). Unlikely but funny alternative.
But because they cut of from Constatinoble they will likely stay Pagan and convert to Catholism in time.
Yes, Novgorod would convert sometimes in early 11th century (they're too big and powerful for Crusade to succeed but it would be too bothersome for them to trade with now-baptized Northern Europe)
Likely North Russia will become part of Scandinavia/Norden purely cultural, even if they keep their own languages (which isn't a sure thing).
We're talking about Polish scenario, more or less. Poland didn't become part of Norden, why should Slavonia (Novgorodian Republic)?
The Jewish states in the south will likely become victims of nomadic invaders
This would depend on relationships between *Khazars and *Rus. Unified state could be just enough to stop Mongols at Volga
