If you believe Arabs are too fond of blaming their homegrown woes on foreigners, don't read this article by Alvaro Vargas Llosa at the Independent Institute. Not that Vargas Llosa is an Arab, but here's his thesis: "It was outside interference that destroyed freedom in the Arab lands." I wish the piece were better argued, but he has one great insight—that the difference between Islamic achievement (until the Ottoman Empire) and Islamic decline (during the Empire) is the difference between decentralized and centralized control.
There was no central authority, therefore no empire. There was no politically organized religion, therefore freedom of cult. People went about their business, whether in agriculture, industry, commerce, or science. Under no political mandate, farmers were constantly fertilizing and irrigating land, and rotating crops. The result was an abundance of food. The towns produced everything from tempered-steel and porcelain to cotton and leather goods. Entire cities thrived on commerce, from the Far East to Saracen Italy (the southern tip) and Saracen Spain.
I think it would be more accurate to say "There was no politically organized religion, relative to Europe at the time." You'd be hard pressed to find a more illiberal dynasty than the Almoravids, who forced even men to wear veils and burned every book but the Koran. But it only makes sense that the Arab achievements in math and the sciences and so on could not have happened without a great degree of intellectual freedom. I'm still waiting for Umberto Eco to reheat his Catholic/Protestant/Mac/DOS analogy to describe the Shiites and the Sunnis.