My question is (now I'm simply gathering sources for my own TL) how the Romans would have viewed an Islam that was more like Eastern Orthodoxy in outward appearance? If the Rashidun Caliphate had survived for longer, keeping up its dhimmi/convert-friendly policies instead of the Arabization and marginalization of dhimmi communities overseen by the Umayyads, I don't think it's beyond the pale to imagine that the large amounts of dhimmis in the government bureaucracy and trading with their Muslim neighbors to exert a heavier influence on the young faith. Certainly nothing core doctrinal, I don't think those kinds of changes would be acceptable to the early Muslim faithful, but something like increased veneration of relics, the presence of Byzantine-influenced paintings of Muhammad and Jesus in masjids, and other "window dressing." I mean, the earliest Muslims were quite in awe of the Romans for being an old and powerful kingdom of People of the Book, even if they did view them as having strayed from the true message of Jesus Christ. The Chapter of the Romans in the Qur'an opens by consoling the Muslims over the Roman loss at Antioch, the Prophet Muhammad had a day of celebration in honor of Heraclius' success in the Cappadochian Campaigns, and Khalid ibn al Walid frequently eulogized the Roman counterparts that he vanquished in poetry. Clearly the Muslims didn't hate and fear the Romans the way the Romans hated and feared them, though tbf, it's easier to be gracious when you're the one doing the curb-stomping.
My guess would be that the Romans would be more inclined to keep up their belief that the Muslims were just weird Christians if they look more Christian from the outside. Would we see a detente between a Romanized Caliphate and the ERE? The ERE could turn its focus westward and the Rashidun would serve as a useful drain-tap for heretical Christians, who could simply move to the Caliphate, pay the jizya, and be left alone instead of constantly agitating in the Roman Empire.
Given the way the Quran speaks highly of the Romans, were any early Muslims opposed to fighting them?