To support the idea that there is no single Islam, some point to the varied behavior of Muslims and the contradictory aspects of the Qur'an (tolerant verses as against totalitarian verses). Other analysts claim such contradictions are resolved by the Qur'an itself, and point to the Qur'an's own doctrine of abrogation (Qur'an 2:106 and 16:101). Thus many Muslim scholars of Islam teach that the militant and totalitarian verses produced later in Muhammad's career abrogate (cancel) the tolerant verses produced earlier in his career. From that point of view, there are no real contradictions and in the end only one Islam, the totalitarian, final, perfected Islam.
However, Bill Warner, who runs the Center for the Study of Political Islam, balances against the doctrine of abrogation a contrary perspective: many Muslims take everything in the Qur’an as eternally true. Warner concludes that Islam is dualistic, not logically consistent. A Muslim can believe two contradictory things at once, so long as the contradiction is present in the Qur’an. From that point of view, while the doctrine of abrogation does to some extent resolve contradictions, it is simultaneously true that it doesn’t — that the whole Qur'an, including both sides of any contradictions in it, is considered by Muslims eternally true. Allah is so dictatorially all powerful that he is not bound by anything, not even logic.
But having found the Qur'an at least somewhat contradictory and dualistic, does Warner stop there? Does he claim there is no single Islam? No. That would be too imprecise an answer. Warner comes out of a scientific background, and tries to drill down into the details. He takes a statistical approach, and looks at the trilogy of core Islamic texts — Qur'an, Hadith, Sira — quantitatively, asking how much of the trilogy is tolerant and peaceful, versus how much is totalitarian and violent. He finds that the percentage of tolerant statements is quite small, of totalitarian statements quite large. So although he doesn’t say there is one Islam, he does find an overwhelmingly predominant form of Islam. For example, in the most canonical hadith collection, Sahih al-Bukhari, Warner finds that over 98% of jihad hadiths refer to violent jihad. This confirms historian Bernard Lewis’ similar contention that in the core Islamic texts, “jihad” almost always means military jihad to defend or expand Muslim power.
So Warner's view, by getting into specifics, really goes beyond the imprecise alternatives: Islam is One/Islam is Many.
Another perspective that influences the debate about this question is what might be called the "decontructionist" view. Even if you don't know what the philosophy of "deconstruction" is, there's a good chance its claims have seeped to some extent into your consciousness by a sort of cultural osmosis. The deconstructionist viewpoint is that a text can be interpreted in an infinite number of ways and can mean just about anything.
The more one thinks about that claim, however, the more it seems a gross exaggeration. While texts have elasticity of meaning to varying degrees, such elasticity is hardly infinite, and that is even more true with texts that are not largely poetic or mythical in content. The Qur'an, Hadith, and Sira are full of quite literal statements and commands. Because of that, Islam's texts and past history have virtually always steered most interpretation into fairly similar and fairly definite grooves. Islam is not whatever one wants it to be. It is a rather definite historical reality. Many years ago, the eminent historian Bernard Lewis wrote of Islam's inherent totalitarianism.
So we should not go to the deconstructionist extreme of suggesting that anything can mean anything. While Lewis Carroll or some other fantasist might be able to treat Islam's core texts as almost a blank slate on which one could write just about any meaning whatever, the people who most seriously and religiously approach Islam's texts generally go by what the texts actually say. Minor ambiguities of meaning dispersed throughout those texts do not erase their clear overall thrust.
So is there one Islam? Are there many Islams? The answer is much closer to the first alternative, though the second has some validity. The bottom line is that, despite real diversity among Muslims globally, there are also overwhelming commonalities of interpretation worldwide, as numerous international polls of Muslim opinion have shown. While there are many liberal Muslims, totalitarianism, to one degree or another, is and always has been the majority interpretation. It is no accident that the core Islamic region of the world has the worst human rights record of any region on the globe: Islam's core texts, despite some vagaries, at bottom teach an expansionist theocratic totalitarian program.