In the end, you will have one of the two encompass the other. Either you have a secular country living by democratic, progressive law which allows people to be Muslims modulo this. Or you have a Muslim country living by Shariah law, but tolerating secular non-believers in it.
First won't work because Muslims (in the traditional sense) won't tolerate some other framework encompassing their worldview. They have taboo topics nobody should ever question, and secular ideology based on science will question things.
And second won't work because Shariah law gives very concrete directions on dealing with non-believers.