maybe it'll just be a continued game of chess between the Persians and the Byzantines?
or will Arabia still be dominated by Constantinopolis, seeing as they (the Arabs) are all at least Christian?
Wait and see!
That's unexpected. I thought Muhammed would unite the Arabs as he did in OTL.
We have a tendency to see historic events through the lens of hindsight, i.e. in light of everything that came afterwards. Because of the phenomenal expansion of Islam IOTL, we tend to see Muhammad as this hugely powerful figure. But we have to remember that at the time of his death, the Muslim community was still very young, small and fragile, and the huge successes it would have shortly thereafter were by no means a foregone conclusion.
It is an exaggeration to say that Muhammad "united the Arabs" IOTL. At the time of his death, he had control over the Hedjaz in Western Arabia. He had contacts with, but no control over, other areas of the Arabian peninsula. And there were many Arabs, mostly under Roman or Persian rule, who had not even heard of Muhammad yet. As soon as Muhammad died, there was significant disintegration in the young Muslim community. Tribes refused to pay the
zakat tax, pointing out that they had sworn allegiance to Muhammad, but owed nothing to his successor. Several rival leaders started to appear, claiming prophethood. This lead to the Ridda wars, which were won by the first caliph Abu Bakr, thanks in large part to Khalid ibn al-Walid, arguably the best Arab general of his time.
It took quite a bit of skill (and luck) from Muhammad's successors to keep things together and really lay the groundwork for the rapid Arab expansion. And that was with the new religion of Islam, which at least for a while helped overcome the traditional Arab tribalism and infighting. A unifying force the Arabs do not have ITTL.
So no Arab conquests makes a HUGE butterfly the size of an elephant.
Please do not jump to conclusions. There will still be Arab conquests ITTL, due to demographic factors that were independent of Islam and are therefore still present ITTL. But the Arabs won't be as unified as they were IOTL, and their conqests will be smaller as a result.
But why several variants of Christianity in Arabia? If Muhammed was the most influential man among the Arabs his successor might be the head of the most influential Christian community, maybe mostly with religious influence, like Pope of the Arabs or something like that.
Religious movements have a tendency to split. IOTL, the Muslims split into Sunnis and Shiites less than fifty years after Muhammad's death. And ITTL, we don't even have a homegrown Arab religious movement, but several Christian churches in the region - Chalcedonian, Miaphysite, Nestorian - potentially vying for the Arabs.
But I don't want to give too much away yet. Rest assured, your will know the answers to your questions when you read the next updates.