Perhaps if the Eastern Romans never lost control of Italia Emperor Maurice's plans of dividing the Empire between his sons would have gone through and their could have been a revived Roman state in the west. Assuming this state survives or doesn't get reabsorbed (which is certainly possible) I don't think it unlikely at all to imagine that this could foment a schism between east and west, with the Emperors in Rome and Constantinople competing over who gets to appoint the Popes and if the Pope in Rome has authority over the other autonomous churches, most importantly Constantinople. It's also important to consider the status of the other churches in the Pentarchy, Antioch, Jerusalem, and Alexandria, and what their stances would be since they aren't subordinate to Muslim rulers in this timeline.