My rambling thoughts, I spent all that time streaming consciousness so I feel obligated to post!
There has been a very healthy (and in some cases unhealthy) symbiosis between western civilization and Christianity over the centuries.
Christs message to follow him and his example doesn't really lend itself to using the government to construct heaven on earth IMHO.
The early church "fathers" Augustine and Aquinas were very much steeped in Greek philosophy. This unholy alliance between church and state is where things went off the rails. In that type of alliance the state always eats the church, the message of Christ being utterly lost. The first healthy step was the Protestant reformation that rejected the authority of Rome. The second healthy step was the US constitution that both separated church and state (institutionally) and provided acknowledgement of the churches important role in society by defining its free exorcise as worthy of enumeration.
While I appreciate those early works of Christian theology and philosophy, as well as enjoy the classics in philosophy, I do believe the church needs to be independent of the state. American Roman Catholics for the most part get it, not up on world wide Catholicism to speak to Romes position on the issue.
Like in the Doctors Hippocratic oath I believe the states first duty is to do no harm. I also believe the government that governs least governs best. Finally like those in our history pointed out, our Republic was designed for and will only work with a moral people. We ceased to be a great nation when we ceased to be a good people.
There is no history of Islam where the prevailing philosophy of "give unto Caesar that which is Caesars, give unto God that which is Gods" has been practiced. The only exceptions are where Muslims are a minority.
From what I can gather, Islam by its very dogma is political and seeks to become "Caesar" so that the force of the state can be used to bring everything into submission to Allah.