Is Islam Compatible with a Free Society?

The Adventures of Chester asks this key question because the way we answer guides us to very different actions:

To say yes to our question, one assumes that there are aspects of being Muslim and faithful to Islam, that can coexist peacefully with liberty, tolerance, and equality. The strategy that follows is one of identifying the groups and sects within Islam that adhere to these notions of their religion, and then encouraging them, favoring them, propagating them, and splitting them off from the elements of Islamic practice that are all too incompatible with the portions of modernity that invigorate men's souls: free inquiry, free association, free commerce, free worship, or even the freedom to be left alone.

To answer no, one states that Islam itself is fundamentally irreconcilable with freedom. This leads to a wholly different set of tactical moves to isolate free societies from Islam. They might include:
-detention of Muslims, or an abrogation of certain of their rights;
-forced deportation of Muslims from free societies;
-rather than transformative invasions, punitive expeditions and punitive strikes;
-extreme racial profiling;
-limits on the practice and study of Islam in its entirety
And even some extreme measures if free societies find the above moves to be failing:
-forced conversion from Islam, or renunciation;
-colonization;
-extermination of Muslims wherever they are found.
These last are especially ghastly measures. But a society that thought Islam incompatible with freedom might in the long term slip towards them.