Does not a theocracy require a mystical belief structure to exist?

Theocracy is a form of government in which a deity is the source from which all authority derives.

In Objectivism, to Objectivists, Self is the origin of all things so to seek or cede authority outside Self (particularly something mystical) is irrational.

What I was attempting to get to is that a theocracy isn't technically a religion (It's a theocracy. There is a clear difference.), and should therefore not be covered under freedom of religion. Why do politicians on both sides give Islam a pass when Sharia Law is clearly prohibited under our constitution and it is inseparable from Islam?

I would suggest that its because people here look at either as irrational whereby they discount/invalidate both. Besides, you can't have a theocracy without a religion and here one religion or faith is as irrational as another.

Theocracy is religious. No crime should be 'protected' just because it is motivated by religion. Any 'protection' for religion is far too narrow. All freedom of thought and speech should be protected without any special status for religion.