I agree with Petike.
The major "Political" effect of Islam was that united the Arabs into a powerful force, that expanded into the rest of the Middle East, into North Africa, and even Spain. No Islam means that expansion doesn't happen, and the Arabs remain disunited. The Arabic language does not spread out of the Arabian peninsula.
In your TL, the Middle East (at least at first) remains dominated by the Christian Byzantine Empire (who also dominate North Africa) and the Zoroastrian Sassanid Empire.
And that time the major Christian leaders were the "Metropolitans", the bishops of Rome, Jerusalem, Constantinople, Antioch, and Alexandria. If one of these got out of line the other four could usually bring them back. In OTL the Islamic expansion into Jerusalem, Antioch, and Alexandria left only two of these leaders, in Rome and Constantinople, which led to disputes between the two and ultimately a split between "Western" and "Eastern" Christianity. But if there is no Muslim expansion into the Middle East and North Africa, the more stable arrangement of five metropolitans would last longer, and the split might never happen.
But having said that, at the time Spain was ruled by the Visigoths, who were not supporters of the Christianity of the Roman Empire, with its Nicene Creed, but instead adhered to a variety of Christianity called Arianism (after its founder, Arius). If Visigothic Spain is not conquered by the Muslims, then the Arian version of Christianity would survive longer.
KEVP
