Mohammedanism was a heresy:  that is the essential point to grasp before going any further.  It began as a hersey, 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.  Its vitality and endurance soon gave it the appearance of a new religion, but those who were contemprary 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 hersiarchs, a man of Catholic birth and doctrine to begin with.  He sprang from pagans.  But that which he taught was in the main Catholic doctrine, oversimplified.  It was the great Catholic world—on the frontiers of which he lived, whose influence was all around him and whose territories he had known by travel—which inspired his convictions.  He came of, and mixed with, the degraded idolaters of the Arabian wilderness, the conquest of which had never seemed worth the Romans’ while… ~Hilaire Belloc (via John Derbyshire)

It is not only the case that St. John of Damascus listed Islam as the 100th heresy in his De haeresibus.  St. Anastasios of Sinai in some of the first patristic references to Islam described Islam principally in terms of its Christological errors–which he likened to Nestorianism–and blamed the rise of Islam on (who else?) the monophysites, because their extreme heresy had, as Anatasios saw it, forced the Arabs who came into contact with them to adopt the equal and opposite heresy.  This is probably not exactly the case, though I believe it is generally accepted that Muhammad learned what little he knew of Christianity from a Nestorian monk whom he met along the caravan routes north.  In any case, Islamic objections to Christianity are those of any anti-Trinitarian heresy mixed with Arian denial of Christ’s divinity and Nestorian contempt for the Mother of God.  I doubt that Islam derives directly from any of these in any measurable way, but it is not entirely ridiculous to think that the domination of Yemen by the monophysite Ethiopians could have influenced how Arabs in that region perceived Christianity and influenced them in such a way that pushed them towards an intense hostility to the idea that Christ was God.  Naturally, Podhoretz ignores the potential relevance of Belloc’s observation to the discussion of the nature of Islam and satisfies himself with an anecdote reminding us that (surprise!) Belloc didn’t like Jews (gosh, nobody knew that!).  Of course, it is not entirely clear to me why Derbyshire thought to bring this up, but it is an idea that is neither far-fetched nor without basis in the Christian tradition of anti-Islamic polemics.