The founding fathers of the USA who were virtually all Christians, did everything in their power to prohibit a "State Religion" because they believed in the New Testament concept of a sin nature. Because of this biblical belief, they knew that power tends to corrupt and absolute power corrupts absolutely. They tried to disperse authority as much as possible among the electorate and government.
There was no separation of Church and State like many like to try and portray. The Christian faith was the foundation period. Morals, ethics, and laws were all based and rooted in the Word of God and were found at every level of every branch of government and school house. They tried to incorporate and balance the OT & the NT models of Law vs. Mercy into its statues.
They gave birth to incredible concepts that:
1. All people were created equal
2. Freedom wasn't something granted to you by a ruler (religious or secular), it was bestowed on you by the Almighty at conception
3. People different than you have intrinsic value because they were made in the image of God
4. There was no need to micro-manage everyone because people believed in a personal judgement after you die
5. God paid a big price to allow people the agency of free moral choice. Consequences not elimination should be emphasized when possible.
6. The Christian faith was to be lived out peacefully, non-violently. Wars were for defence, not for the spread of a particular form of government or religion.
A Lot of our history fell short of these ideals, much of our history rose up to the occasion too though.
Islam, from what I know of it seems the antithesis of the traditional American (and now much of the west in general) value system.
It seeks a state religion through Sharia Law. From its beginning, it spread by violent conquest. By contrast Christianity took down the most powerful military machine the world had ever known - Rome: without a single sword being drawn. The two systems couldn't be more different.