The establishment of religious freedom goes way back to before Christ and was established numerous times in different places around the world. The Declaration of Independence only set a precedent for freedom of religion in relation to the United States. The Declaration of Independence did not set a precedent for Religion in Government.
While the Declaration of Independence does make some reference to God-given rights ("endowed by their Creator...") it was never intended to be a document that would set the course for American government. It was simply a note from our high level businessmen and politicians telling the King that enough is enough, we're leaving, goodbye. The First Amendment in the Bill of Rights is proof enough that religion was never intended to have a place in government.