There's a good chance the crusaders wouldn't initially know the difference or care. Keep in mind that any Jewish population in the medieval Levant would have lived under either Muslim dynasties, in which case they'd have been under dhimma and not have borne arms, or under Byzantine and allied Christian rulers, in which case they'd have been subject to the restrictions of the Roman law and also not have borne arms. A Jewish state would be extremely far-fetched. Thus, the most likely outcome is that initially, they are treated as suspect and unnecessary by their Muslim rulers and as infidels by the Crusaders. Later on, the lords of Outremer will treat them much like any other population group, slotting them into the social pyramid somewhere around the level of most inoffensive locals, below local Christians, maybe above Muslims or about equal. Lots of Crusaders came from areas with established Jewish populations and wouldn't have had any great issues with the idea. But the function of cultural interpreter and go-between here could be better served by Syriac Christians, so they'll not be as useful.