What if you have a POD where either the Persians stay Zoroastrian or convert to Christianity, maybe a competent leader just before the Arab invasion. The Arabs also fail miserably when fighting the Byzantines in the Levant.
The Arabs are strong enough to defend their holy cities against the Persians and the Byzantines, but not expand as they did. Maybe they're able to take the Horn of Africa, the east African coast from Somalia to South Africa, on around to Angola which becomes the heart of the Arabian Caliphate with its rich farm land. Its possible to see the Arabs or another Muslim group (perhaps an indigenous African peoples) to conquer west Africa, and have as you said the Sahara as the border between the Muslim world and the old world.
Africa could possibly be somewhat better off for it, the Muslims build roads, grand cities, unite the various ethnic groups under a single religion and language, so there is no more infighting on the same scale as OTL. Plus the arrival of technology from Arabia.
The question is what do you do with the Turks? They are still going to be coming, but they will have to deal with the Persians, meaning its possible that they convert to the Persian religion, would they still be interested in Anatolia? Or perhaps they decide to settle in Mesopotamia. It would make it interesting if they didnt convert to the Persian religion and adopted Islam, or if the Persians are Christian they convert to Zoroastrian when they settle. Or the Turks cant pass through Persia so go through Russia or go east, perhaps eventually discovering Australia?
What of the America's? Without the Moor Conquest of Iberia, there will be no Spain as we know it, I wonder if the Goths would be interested in exploring the America's. The British and French are a safe bet, perhaps somewhere in this ATL there is a successful reformation of the Western Roman Empire that is very interested in the new world.