Fred Kagan articulates clearly the fissure between al-Qaeda’s ideology and traditional Islam:

Al Qaeda’s ideology is the lineal descendant of a school of thought articulated most compellingly by the Egyptian revolutionary Sayyid Qutb in the 1950s and 1960s, with an admixture of Wahhabism, Deobandi thought, or simple, mainstream Sunni chauvinism, depending on where and by what group it is propounded.Qutb blended a radical interpretation of Muslim theology with the Marxism-Leninism and anticolonial fervor of the Egypt of his day to produce an Islamic revolutionary movement. He argued that the secularism and licentious (by his extreme standards) behavior of most Muslims was destroying the true faith and returning the Islamic world to the state of jahiliyyah, or ignorance of the word of God, which prevailed before Muhammad. The growing secularism of Muslim states particularly bothered him. According to his interpretation, God alone has the power to make laws and to judge. When men make laws and judge each other according to secular criteria, they are usurping God’s prerogatives. All who obey such leaders, according to Qutb, are treating their leaders as gods and therefore are guilty of the worst sin–polytheism. Thus they are–and this is the key point–not true Muslims, but unbelievers, regardless of whether they otherwise obey Muslim law and practice.This is the defining characteristic of al Qaeda’s ideology, which is properly called “takfirism” (even though al Qaeda fighters do not use the term). The word “takfir” designates the process of declaring a person to be an unbeliever because of the way he practices his faith. Takfir violates the religious understanding of most of the world’s Muslims, for the Koran prescribes only five requirements for a Muslim (acknowledgment of the oneness of God, prayer, charitable giving, the fast, and the pilgrimage to Mecca) and specifies that anyone who observes them is a Muslim. The takfiris insist that anyone who obeys a human government is a polytheist and therefore violates the first premise of Islam, the shahada (the assertion that “There is no god but God”), even though Muslims have lived in states with temporal rulers for most of their history. The chief reason al Qaeda has limited support in the Muslim world is that the global Muslim community overwhelmingly rejects the premise that anyone obeying a temporal ruler is ipso facto an unbeliever.Today’s takfiris carry Qutb’s basic principles further. Some pious Muslims believe that human governments should support or enforce sharia law. This is why Saudi Arabia has no law but sharia. But to Osama bin Laden and his senior lieutenant, Ayman al Zawahiri, it is not enough for a state to rule according to sharia. To be legitimate in the eyes of these revolutionaries, a state must also work actively to spread “righteous rule” across the earth. This demand means that only states aligned with the takfiris and supporting the spread of takfirism–such as the Taliban when it was in power–are legitimate, whereas states aligned with unbelievers, like Saudi Arabia, are illegitimate even if they strictly enforce sharia law. Some takfiris, particularly in Iraq as we shall see, argue in addition that all Shia are polytheists, and therefore apostates, because they “worship” Ali and Hussein and their successor imams. This distorted view of Shiism reflects the continual movement of takfiri thought toward extremes.

Fred’s piece is very worth reading and it’s here.