"The Cordoba Initiative, which is headed by an imam named Feisal Abdul Rauf, is an enemy of al Qaeda, no less than Rudolph Giuliani and the Anti-Defamation League are enemies of al Qaeda. Bin Laden would sooner dispatch a truck bomb to destroy the Cordoba Initiative's proposed community center than he would attack the ADL, for the simple reason that Osama's most dire enemies are Muslims. This is quantitatively true, of course -- al Qaeda and its ideological affiliates have murdered thousands of Muslims -- but it is ideologically true as well: al Qaeda's goal is the purification of Islam (that is to say, its extreme understanding of Islam) and apostates pose more of a threat to Bin Laden's understanding of Islam than do infidels."
Radical militant Islamist thought isn't fully united on these issues, and recruitment propaganda tends to cast a broad net, but the historically dominant strain has argued that most of the Islamic world has slipped into a state of unbelief and is suffering because of it, and fixing that by enforcing the sort of harsh religious views found in Wahhabism and similar movements is their primary goal. The United States gets involved because we are the "Far Enemy" whose cultural, economic, political, and military policies interfere with that project of internal conversion.
Here's another Goldberg post on the subject.
(Crossposted to American Footprints)