The difficulty, of course, is that Islam is not like Christianity. It does not recognize any difference between Church and State.
Even when you have an Established Church in the West, there is still some separation--kings and presidents on one side, bishops on the other. In Islam, there is no separation. They never understood that saying of Jesus: "Give unto Caesar that which is Caesar's, and unto God that which is God's."
Allah demands everthing, without exception, and the head of state is Allah's representative on earth. Islam calls on everyone to submit.
Maybe this conundrum can be solved, but it won't be easy.
Islam is thousands of years old. It's not going to happen in our life time - if ever!