Nowhere in the Constitution does it make any distinction between public and private, personal and official respecting freedom of expression or freedom of speech.
Article. VI.The Senators and Representatives before mentioned, and the Members of the several State Legislatures, and all executive and judicial Officers, both of the United States and of the several States, shall be bound by Oath or Affirmation, to support this Constitution; but no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States.
What they may not do is endorse or support specific religious viewpoints in their official status. That is not "free expression", but Establishment.
How is it establishment? Endorsment or support of an existing viewpoint hasn't created the view so it isn't establishing it. It doesn't make a law requiring reverence or adherence to a viewpoint so it isn't coercive and therefore establishes no government authority respecting the viewpoint. It doesn't effect the source of the viewpoint so it is neutral respecting a previous or private establishment of religion.
Endorsement and/or support without the means to coerce either acceptance or rejection of a religious view is nothing more than expression. The only means government has to rightly coerce anyone in anything is by the law and there are no laws requiring acceptance or rejection of any religious view. Only Congress can make laws and Congress is expressly prohibited from making any law respecting an establishment of religion.
To prohibit acknowledgment of God in any forum is to make law respecting an establishment of religion. As far as Judge Moore goes he set no precedent on behalf of government in terms of acknowledging God as a higher authority than government. The Declaration of Independence itself does that.
The Declaration of IndependenceWe hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, ...
There it is in black and white: the source of our Rights is our Creator. Define Him/her/it as you will they don't come from men or government. Now here are some of the Rights that it refers to:
Amendment ICongress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.
Where is there any possible inference of the meaning of the word 'establishment' in the simple acknowledgment of God by prayer, picture display or by display of a monument? 'Express' and 'establish' are not synonyms and mean very different things unless the meaning of 'is' isn't is anymore.