MoodVertigo wrote a really long comment over at my Answering a Fifth Comment Regarding the Pledge entry. It’s really long, so I’ll only go over it piece by piece.
Alright, I’ll make this really basic. For the sake of argument, let’s assume all your reasoning is correct, specifically: “The First Amendment only limits Congress; no one else.”
From The Pledge of Allegiance A Short History, we learn that, “In 1954, Congress after a campaign by the Knights of Columbus, added the words, ‘under God,’ to the Pledge. The Pledge was now both a patriotic oath and a public prayer” [emphasis mine]. Okay, so Congress specifically made a “law respecting an establishment of religion,” got it?
It does respect an establishment of religion because, first of all, any god equals religion. Second, as I’ve mentioned before, “God” is a proper noun, a specific name. We would not approve of “under Allah” in the Pledge of Allegiance, so we should not approve of “under God”.
Even under your reasoning, the words “under God” in the Pledge of Allegiance are still unconstitutional.