Absolutely incorrect ... and a neophyte's mistake.
Read the First Amendement's religion clause again -- this time with correct application of the rules of English grammar, syntax and vocabulary -- and you should easily see, I hope, that the word "establishment" is a noun, not a verb.
Simply follow the rules of English grammar, syntax and vocabulary, and the Constitution reveals itself without any need to ideologically exit the Constitution for "reference" ... and this was just how the writers as a community group intended.
We can't have the SCOTUS quibbling over its imagination of what is "common interpretation" ... as such is subject to preconceived ideological filtering.
And if Manny Moron says that having a group conversation with God is a "religious" practice just because he thinks so, that's no reason to override a recent unanimous decision by a recent modern council of duly authorized representatives of every religion in the world, a unanimous decision that reference to God is not indicative of a philosophy being a religion.
The SCOTUS, as does the Constitution, must allow for changing times and stay current in referential vocabulary translations, and not merely appeal to archaic errors of perception that are, thus, no longer applicable when revealed or that appeal to the lowest common denominator.
And prayer looks like it does everywhere because of the way 'men are made and God is, whether the prayer is being performed within a religious ceremony or not, so a "prayer session", by descriptive nature, can only be "religious" if performed in association with religious articles.
Keep in mind that prayer is the function of "speaking" to God, just like meditation is the function of "listening" to God.
Your libertarian bias is obvious here in your implied blind worship of private enterprise that causes you to miss the clear text of the Constitution that authorizes the federal government to coin money.
Whether the fed farms out the process to a private company is absolutely irrelevant.
That private company does not have the right to "coin" money, nor does it have any say in what is inscribed on our money.
The Constitution authorizes the federal government to create statutes that describe what is to be on the face of each piece of money. Thus the fed itself authorizes what is to be printed on the money, not some private company, and so the fed alone is responsible for our money's depiction.
So the appearance of God on our money is not because some private company made that decision, a private company being "separate" from the federal government -- that's simply preposterous .
Was there ever any.