I know this is kind of a cop-out:
How about a religion arises is Arabia which has the same uniting force that Islam did, but is based on Arabic tribal religions rather than Judeo-Christian monotheism (so it's not Abrahamic). Then, it 'pulls an Islam', and expands as far as the Balkans and Iberia, but ends up more successful than OTL Islam and successfully converts most of Europe.
I guess what I'm really trying to say was that I don't feel that the rapid expansion of Islam depended on it being an Abrahamic faith. It is conceivable that, in an ATL with a 500 AD POD there could be another religion which would arise which would have the same expansionist success that Islam had without being based on Abrahamic traditions.
Certainly any religion which arises in North Africa or West Asia and has the same expansionist success that Islam had could conceivably overtake Europe....