Could Freedom Destroy a Free Society?

It's a good thing, I think, to ponder the details of a free society. So here goes.

Freedom of religion would certainly exist in a free society. Let's imagine that a growing muslim population reached the greatest limit, through peaceful proselytizing, until all members of the free society converted to Islam.

Suddenly, muslim leaders declared Sharia. Would this destroy the freedom of the free society or could a free society exist under such a situation? If every member of the nation wanted to eradicate freedom and live under Sharia, could they or would the constitution remain intact?

Let's get some opinions on this.