Muslims have a different interpretation of history from the modern secular humanist one.
(51) Islam: What factors keep Islam from modernizing? - Quora Monday, October 14, 2013 @ 8:03pm
For example, let's take the events following the Protestant Reformation. Modern Western civilization's roots are in the reformation of Martin Luther (the doctrine of the two kingdoms), the friction between Galileo and the Catholic Church over heliocentrism, the formation of the Church of England and the founding of the United States.
After the behavior of a church that seemed to be doing strange things (selling forgiveness, dismissing scientific evidence), and kings that ruled arbitrarily by divine right, people began to want to create a barrier between the Church and political control.
A Western interpretation of this history, and one echoed in the other answers, is "religious involvement in politics is bad. Our history is universal, every culture will evolve the way we evolved from a religious frame of reference to a secular humanist frame of reference -- the problem is religion itself." This is also echoed in a lot of "modern" political theory, e.g. Francis Fukuyama's The End of History (http://en.wikipedia.org/wiki/The...).
An Islamic interpretation of this history would attribute this break between the church and the state to irresponsible/bad behavior by the Catholic Church, and kings because of the issue of having to resort to papal infallibility and divine right.
They did not have a well-preserved divine source of law to guide them. The Muslim response to the Fukuyaman view is: "The problem isn't religion, the problem was Christianity and monarchy. It was particular to Christianity and your history. We don't have that problem. Your experience is not as universal as you think it is."