Correct but the United States being a nation promulgated from the enlightenment (British not French) requires a seperation of State from Church “Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof;”
That islam believes the opposite that the state is controlled by religion
“Those who participated in secular politics were raising the flag of revolt against Allah and his messenger”
To put it bluntly the Constitution can abide islam but islam can not abide the Constitution. See Surah 9:5 and following.
In essence the difference between Christendom and islam may be summed up by what to my way of thinking is the foundation for separation of Church and State
Matthew 22:21 New International Version (NIV)
21 Caesars, they replied.
Then he said to them, So give back to Caesar what is Caesars, and to God what is Gods.
islam has no such structure.
#35 applies to your reply as well.