First, we must erect a wall of separation between the concepts of a belief in God, and religion; they are by no means one and the same.Actually, belief in "God" is a religious belief. It is of course distinct from atheism, agnosticism, or polytheism.
The next step is a belief that said God intervenes in the affairs of man. The "clockmaker" variety of Deism does not accept this principle, yet Deists believe in God. Incidentally, the "creator" related lines in the Declaration of Independence are not inconsistent with "clockmaker" Deism.
Once intervention is accepted, monotheism branches off into several different variants. The Ten Commandments only apply to Catholics and Jews...though there's nothing in them that would cause a Muslim to object. Moore's selection of the King James Bible version (as opposed to the US Supreme Court which just shows tablets with Roman numerals) further narrows the interpretation.
Every time that Government endorses one or more steps down this path, in any direction (including atheism), Separation is breached.
-Eric