I'd think this is mostlöy a theological matter, at heart. None of the lwas limiting the Jews in their professions, careers, and lives would have come about if the Christian churches had not developed the doctrine that the Jews were responsible for the death of Jesus and therefore were destined to suffer a penalty analogous to that of Cain. The idea started very early in the Roman Empire (mostly, it seems, for the Christians to be able to claim not to be anti-Roman), but it wasn't carried into practice generally till around AD 1000.
If Christianity had found a doctrinal formula closer to that of Islam (ie the Jews are in possession of a lesser degree of truth and must be tolerated and protected) the position of the Jewish population could have become very different. An Arian rather than Athanasian Christianity would have had it easier, but I don't think anything that dramatic is necessary. Given such a change - perhaps at the insistence of Frankish kings, or even the heritage of a revered church teacher - medieval Jews would have suffered fewer limitations, would not have been expelled from France or England, would have been allowed to settle wherever they chose, had a greater freedom of choice of profession, and very likely would have interacted more readily with their Christian neighbours. It is very likely that this was the state of affairs until around AD 800, so a continuation is not all that unimaginable.
I don't think Judaism would disappear as a faith - it didn't in the context of a far more tolerant and welcoming Islamic society until the last 50 years, and then for very different reasons - but it would have to deal with different challenges. cross-conversion would be more of a drain if Christianity were more welcoming, and everyday contact with Christians on the job would create more familiarity and probably undermine religious ritual and dietary law. On the other hand, early bishops of the church often complained that their sheep were going to the synagogues because the sermons were better, and even started keeping the Sabbath...