Understandably, our Muslim brothers and sisters who believe in the uniqueness and truth of Islam might be offended at the suggestion that their religious tradition is reducible to an incorrect Christian belief. Others might be offended not because they see Islam as unique in its practices or truth claims, but because they see religions as roughly equally good or bad, and thus for them the concept of heresy is either meaningless or laughable because in their view religious truth claims are either all true or all false.
As someone who counts faithful Muslims and cultural Muslims among his friends, and someone who has studied Islam and read an English translation of the Qur'an, as well as someone who has prayed with Muslims, I would like to explore the question of whether or not Islam is a Christian heresy in an honest way which is not accusatory or derisive. Unlike the folks who believe that religions are all basically the same (for good or ill), I recognize that Islam makes some unique truth claims in sometimes unique ways. I believe that we should respect Islam by treating it with the seriousness it deserves, because if it is true, then we must change our lives or face horrible consequences.
In answering the question of whether or not Islam is a Christian heresy, we need to examine two issues:
1. Does Islam contain Christian heresy in its core beliefs?
2. If so, then can the whole of Islam be reduced to those core beliefs?
To address the first question, I will begin with the Qur'an. There are verses in the Qur'an which specifically address Christian theological claims, and given that the Qur'an is the authoritative teaching document for Muslims, it would seem that to be a Muslim and therefore to engage in Islam as understood in the authentic tradition of Islamic thought is to accept whatever the Qur'an teaches regarding Christian theological claims.
So what does Islam teach with regard to Christian theological claims? Well, there are multiple verses in the Qur'an that specifically say that Jesus was not the Son of God. And also that Christians who believe this are liable to end up in Hell (Jahannam in Arabic). The belief that Jesus was not the Son of God, but rather a mere creature of God, a holy man sent by God, is indeed a known Christian heresy. Arianism is the most well-known example of a Christian heresy affirming that Jesus was not the Son of God, though it's not the only one to do so.
It is also claimed in the Qur'an that Jesus did not actually die on the cross, but only appeared to die on the cross. This is a Gnostic heresy found in Gnostic texts like the Apocalypse of Peter, for example.
These are both Christian heresies, and both are found stated explicitly in the Qur'an, which is the authoritative repository of Islamic core beliefs. So the answer to Question 1 posed above is, "Yes." Islam contains Christian heresy in its core beliefs.
To address the second question, we need to think about what Islam is as a whole. In order for Islam to be a Christian heresy, it must be a Christian belief system which happens to contain some serious doctrinal error to which it holds persistently. Arianism was a Christian heresy because it was otherwise Christian in every way: in terms of liturgy, Sacred Scripture, ascetic practices, spiritual sensibility, and most doctrines. The same was true of Pelagianism, and a variety of others.
But that simply isn't true of Islam. According to the Qur'an and Muslims who adhere to it, what they are practicing is better than Christianity, a simpler and pure religion that avoids the corruption and perversions of Jewish and Christian doctrines which strayed from the straight path of Abraham (Ibrāhīm in Arabic). Their religion isn't centered around the story of Christ, but rather around the teachings of the Prophet Muhammad revealed in the Qur'an and recorded in the hadith, the accounts of the sayings and actions of the Prophet Muhammad.
Just as Christianity isn't merely a Jewish heresy (though it certainly contains tenets that are heretical from a Jewish standpoint), Islam isn't a Christian heresy, though it certainly contains tenets that are heretical from a Christian standpoint. So the answer to Question 2 posed above is, "No."
No matter what the teachings on Jesus are within Islam, it's not a Christian heresy for the very simple reason that it isn't Christian. In order to be a Christian heresy, it would have to first be Christian in the sense of being centered on Christ, just as I would have to be a Christian in order to be guilty of being a Christian heretic for believing the doctrine of Arius.
To be fair to those who do believe that Islam is a Christian heresy, there is a better argument to be made that most Muslims are by definition heretics from a Christian perspective. While Islam may not be a Christian religion, devout Muslims do have faith in Jesus to a certain extent. They believe that he was a true Prophet sent by God (though his message was corrupted by Christians), that he was born of a virgin named Mary, that he was a holy and righteous man, that God saved him from death, and that he will return with power on the Day of Resurrection.
Is that enough for us to say that Muslims are Christians, and that therefore Muslims would be by definition guilty of heresy for believing that Jesus was not the Son of God? It would seem strange to claim that Muslims are Christians when they generally don't believe that themselves (with perhaps a very small percentage of exceptions).
Though it's certainly true that to be a devout Muslim who believes the teachings of the Qur'an necessitates believing things that contradict the Christian faith, it's also true that Jews, Buddhists, and atheists necessarily believe things that contradict the Christian faith. And while we would say that some of their beliefs are heretical from a Christian perspective, we don't say that Judaism, Buddhism, or atheism is a Christian heresy. So why would we say that Islam is a Christian heresy?
I suspect that Islam is treated differently in this regard because it is the only major world religion to arise after Christianity which has explicitly recognized parts of Christianity as true and also offered explicit theological critiques of Christianity's doctrines in its own sacred text. I understand that, for those reasons, it is tempting to put Islam in the unique position of being the only major religion to be labeled "a Christian heresy" while other religions are only described as having heretical beliefs.
I hope that those who do believe that Islam is a Christian heresy also understand my reasons for disagreeing with their position.
Related: What does the Qur'an say about unbelievers, Jews, and Christians?
The Other Side: Hilaire Belloc's Historical Argument for Islam as a Christian Heresy
Note: The above is an image of a copy of the Qur'an opened to the "Maryam" surah.