Let's say Judaism, during a short period of time somewhen in the 6th/7th century, becomes the predominant religion of the Arabian peninsula, and unites under this religious basis. Let's say that, during or shortly after a Sassanid-Byzantine war, when Persia and the ERE are both weakened, they decided to return the Holy City of Jerusalem into Jewish hands, and this sparks an entire regional conflict in which the Levant and Egypt, and afterwards maybe even parts of Persia, fall into the hands of this Jewish Caliphate.
Is it plausible at all? I don't even that this entity will be as powerful as the OTL caliphate, just that it will see itself as the leader of Judaism, have a Jewish majority, and control much of the middle east.