this is the opinion of Cornell University Law School.
They wrote
The First Amendment’s Establishment Clause prohibits the government from making any law “respecting an establishment of religion.” This clause not only forbids the government from establishing an official religion but also prohibits government actions that unduly favor one religion over another. It also prohibits the government from unduly preferring religion over non-religion or non-religion over religion.
You see, to understand the First Amendment to mean anything but having to do with a State sponsored and controlled denomination, leaves all stances in legal trouble. If you prefer a religion over another or none, or none over any, you have broken the First Amendment according to Niose’s understanding.
Rather, the first amendment guarantees Americans the freedom to express and practice their religion without interference from the federal government. This includes
Two can put up posters, why not put up a few atheist posters, for example
Exodus 35:2
Six days work shall be done, but on the seventh day you shall have a Sabbath of solemn rest, holy to the Lord. Whoever does any work on it shall be put to death.
So shall we kill all the preachers who preach on Sundays?
The phrase "separation of church and state" is not in the Constitution, nor the Declaration of Independence, nor any other law written by the founding fathers of this country. That phrase was written by Thomas Jefferson in a letter to a Baptist Association to assure them that the government would not interfere with their freedom to practice their religion, either in public or private.
Read carefully the clause that is in the Constitution and you will see it states that Congress will not establish an official church (such as the Church of England that was established as the government sanction religion of England) AND that congress will not hinder the free exercise of the citizen's religion.
The early fathers of this country believed and displayed that a person must be able to freely exercise their religion in private, or public; including in government!
Notice these quotes. Notice the importance of religion, specifically the Christian religion in their lives and as a basis for the government they were setting up:
President John Quincy Adams directly addresses the Ten Commandments --"The law given from Sinai was a civil and municipal code as well as a moral and religious code. These are laws essential to the existence of men in society and most of which have been enacted by every Nation which ever professed any code of laws. Vain indeed would be the search among the writings of secular history to find so broad, so complete and so solid a basis of morality as the Ten Commandments lay down."
George Washington - "While we are zealously performing the duties of good citizens and soldiers, we certainly ought not to be inattentive to the higher duties of religion. To the distinguished character of Patriot, it should be our highest glory to add the more distinguished character of Christian."
Thomas Jefferson - "I am a real Christian – that is to say, a disciple of the doctrines of Jesus Christ."
Benjamin Franklin - "I've lived, sir, a long time, and the longer I live, the more convincing proofs I see of this truth: That God governs in the affairs of men. If a sparrow cannot fall to the ground without His notice, is it probable that an empire can rise without His aid? We've been assured in the sacred writings that unless the Lord builds the house, they labor in vain who build it. I firmly believe this, and I also believe that without His concurring aid, we shall succeed in this political building no better than the builders of Babel."
James Wilson (Signer of both the Declaration of Independence and the Constitution; Original justice on the U.S. Supreme Court) - "Human law must rest its authority ultimately upon the authority of that law which is Divine ... Far from being rivals or enemies, religion and law are twin sisters, friends, and mutual assistants. Indeed, these two sciences run into each other."
Joseph Story: (U.S. Supreme Court Justice; "Father of American Jurisprudence," Placed on the Court by President James Madison) - "One of the beautiful boasts of our municipal jurisprudence is that Christianity is a part of the Common Law ... There never has been a period in which the Common Law did not recognize Christianity as lying at its foundations ... I verily believe Christianity necessary to the support of civil society."
House Judiciary Committee Report, March 27, 1854 - "At the time of the adoption of the Constitution and the amendments, the universal sentiment was that Christianity should be encouraged...In this age there can be no substitute for Christianity...That was the religion of the founders of the republic and they expected it to remain the religion of their descendants."
John Hancock - "Resistance to tyranny becomes the Christian and social duty of each individual. ... Continue steadfast and, with a proper sense of your dependence on God, nobly defend those rights which heaven gave, and no man ought to take from us."
John Q Adams - "The hope of a Christian is inseparable from his faith. Whoever believes in the divine inspiration of the Holy Scriptures must hope that the religion of Jesus shall prevail throughout the earth. Never since the foundation of the world have the prospects of mankind been more encouraging to that hope than they appear to be at the present time. And may the associated distribution of the Bible proceed and prosper till the Lord shall have made 'bare His holy arm in the eyes of all the nations, and all the ends of the earth shall see the salvation of our God' (Isaiah 52:10)."
Alexander Hamilton - "I have carefully examined the evidences of the Christian religion, and if I was sitting as a juror upon its authenticity I would unhesitatingly give my verdict in its favor. I can prove its truth as clearly as any proposition ever submitted to the mind of man."
George Washington - "It is the duty of all nations to acknowledge the providence of Almighty God, to obey His will, to be grateful for His benefits, and humbly to implore His protection and favor."
John Adams - "We have no government armed with power capable of contending with human passions unbridled by morality and religion. Our Constitution was made only for a moral and religious people."
James Madison - "Before any man can be considered as a member of civil society, he must be considered as a subject of the Governor of the Universe."
John Q Adams - "Is it not that in the chain of human events, the birthday of the nation is indissolubly linked with the birthday of the Savior? - that it forms a leading event in the progress of the Gospel dispensation? Is it not that the Declaration of Independence first organized the social compact on the foundation of the Redeemer's mission upon earth? - That it laid the cornerstone of human GOVERNMENT upon the first precepts of Christianity."
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As you noted, God is mentioned on our money, and many prominent places in our government.
God is acknowledged in the Declaration of Independence, the US Constitution, and the constitutions of ALL 50 states. There are biblical references etched into many of the national monuments, every President of the US was sworn in with their hand on a Bible and promised to fulfill their duties "so help me God"!
The Bible, and Bible stories were used as text in schools from the founding of our nation, and it has only been about the last 40 years that people have fought to restrict it. (Remember the Constitution says Congress can make no laws to restrict the free exercise of religion.) Bible references, stories, and principles were part of the famous McGuffey Readers that were used as official textbooks in public schools from the 1830's until 1960.
On September 6, 1774, the first act of the first session of the Continental Congress was to pass a resolution to open its next meeting with prayer.
On September 11, 1777, the following recommendation was approved by the Continental Congress
...the use of the Bible is so universal, and its importance so great, ... the committee recommend that Congress will order the Committee of Commerce to import 20,000 Bibles from Holland, Scotland, or elsewhere, into the different ports of the States of the Union.
There are so many references that could be given that they could fill page after page! These, however, are enough to show that the fathers of this nation say religion as an important and vital part of not only private life, but public (including government) also!