We could have Muhammed convert to Coptic Christianity somehow, before he founds Islam. He helps convert Arabia to Christianity. Of course, Judaism will grow as well.
No need for any Conversions.Wasn't this sort of thing one of the premises Turtledove had in Agent of Byzantium? He had St. Mohamet be a convert to Christianity when he was a trader visiting Syria, then end up as a hymn-writer, bishop of Ispania, and patron saint of changes.
Turtledove forgot that Mohammad started out as a Cristian reformer [like Luther 1000 years later]
After disagreement with the Bishop of Mecca, Mohammad was kicked out of town.
He was taken in by the Arab tribesmen where he learned about Allah, and wrote his reformed religion.
Avoid the argument, or the taking in by the Tribes, and Islam never comes, or comes very different.
In the first decade of the 500's one of the Yemini rulers converted to Judaism, This lead to a war with Axum, where Axum Conquered Yemen.That isn't the problem, the problem is that even the "heretical" Christians who hate Constantinoble will fight to the death against the Jews. But the question is academic because the Arabs will first turn Jewish after the Arab Eruption, so we likely just see a few short term Arab Kingdoms in the Crescent.
Have this war go different and you get a large prosperous Jewish kingdom at the south end of the red sea. 150 years before the Eruption.