Islam has never been known to have been considered as a sect of Christianity. St John of Damascus neither considers Islam to be a sect nor a separate religion; rather he plainly refers to Islam as a Christian heresy in his writing “the heresy of the Ishmaelites”.
His assessment would be most pertinent to consider, as St. John of Damascus is from Islamic neighbourhood and possibly a witness as to how Islam was moulding and adapting itself from its nascent stage. This is evident from the fact that he even refers, most interestingly to one sura (called the ‘Camel of God’) which is no longer extant in present day Quran.
Another reference to Islam as a heresy of Christianity comes from Belloc's view, who identifies it as a heresy in The Great Heresies. To quote from this briefly:
Mohammedanism was a heresy: that is the essential point to grasp
before going any further. It began as a heresy, not as a new religion. It
was not a pagan contrast with the Church; it was not an alien enemy. It
was a perversion of Christian doctrine. It vitality and endurance soon
gave it the appearance of a new religion, but those who were contemporary
with its rise saw it for what it was_not a denial, but an adaptation and a
misuse, of the Christian thing. It differed from most (not from all)
heresies in this, that it did not arise within the bounds of the Christian
Church. The chief heresiarch, Mohammed himself, was not, like most
heresiarchs, a man of Catholic birth and doctrine to begin with. He
sprang from pagans. But that which he taught was in the main Catholic
Apart from above historical citing, it is apparent that Christianity and Islam differ on every aspect, regardless of what Islam tries to portray. Contrary to the general impression that they are both Abrahamic religion, they have diametrically opposite perception on the whole lot, be it personalities OR events from the Bible. The commonality is only in the “names” of personalities from the Bible which are cited in Quran, with no sameness in the perception of who they were and what they did. It is literally on the semblance of only names that people are trying to label Islam as Abrahamic religion which is irrational and to term it as a sect of either Judaism or Christianity is at its nadir.
Mohammad was from a clan that believed in one of the Christian-Jewish heretic sects. All that Mohammed did was to adopt all the revered and common names from Judaeo-Christian scripture into his imitated teaching, with a hope to lure the Jews and Christians to follow him and the identicalness ended there and there. So also to lure Arabs, some substance was taken from Pre-Islamic Pagan peoples who were worshiping moon god.
On any major topic from Bible, Quran has a different story to tell. If one takes the event of sacrificing of Isaac by Abraham, Nature of God, accepting Gnostic literature discarded by Christians, Jesus’ death, resurrection and so on. The most contrasting view is found in what Jesus taught and teaching in Quran. They are not at all compatible with each other but at two divergent points. Most importantly, life of Jesus is full of grace and that of Mohammad is contrary.
It is unrealistic to even bring them on same platform or say Islam is a sect of Christianity.