NO. Islam as Islam (a system of total control of every aspect of life) is completely incompatible with any other system of organizing and governing groups of people. Apostate Islam can slide by for a while until someone starts reading and acting on the Quran, Hadiths, etc.
Second question: "Can a post-Christian secular West continue to exist with neither a moral compass nor any objective basis for civil behavior and society?"
CONSTITUTIONAL RIGHTS FOUNDATION - The Hebrews and the Foundation of Western Law
I was having a discussion yesterday with someone about this very thing. I do not believe that free societies were ever meant to operate without Judeo Christian principles.
Freedom does not mean to function free from God, it means to live freely, UNDER God’s ways. The controls really need to come from God living within us.
I think the cultural decay we are witnessing in both of our countries is the result of freedom, WITHOUT God’s influence.