Wouldn’t a Christian nation of absolute necessity prohibit free exercise of religion?

If (as Nano and others repetitively suggest) America constitutes a Christian nation, why does our constitution prohibit the establishment of a national religion? The first commandment, after all, reads “I am the lord your god, you shall have no other gods before me”.

We similarly haven’t legislated that American citizens keep holy the Sabbath, avoid taking the Lord’s name in vain, honor our fathers and mothers, etc. In fact the only commandments supposedly received from god that are incorporated into civil law are those that are entirely non-religious in nature: do not lie, do not steal, do not commit murder, etc. (legal prohibitions common to the vast majority of human societies, regardless of whether or not those societies are Christian or not.)