The 1st amendment supports that the separation of church and state is mandatory. The United States of America was formed on the principle of religious freedom (ex. The pilgrims were seeking escape from persecution), through the most rational way possible: through secularization of the government. Also, when they say "in God we trust" they never specify WHICH god. It could just as easily be Allah that they are talking about then it is the Christian god. Also, the "in God we trust" bit wasn't added until the American Imperialism era, when religious and racial superiority were everywhere: even in our own government (sadly).
The principle of separation of church and state is mandated by the constitution. The first amendment specifically addresses this subject. Not only that, the founding fathers have been quoted saying that there should be a wall between the church and the state. If you do not believe this just go and read the first amendment.
The phrase "separation of church and state" came from a letter written by Thomas Jefferson, in 1802, to Baptists in Danbury, Connecticut. The Baptists heard a rumor that there was going to be a national Christian Denomination set up. He answered that it was not true and there would remain a "separation of church and state."
Regarding your comment saying "if you do not believe this, just go read the First Amendment", I did, and it says "Congress shall not pass pass a law respecting an establishment of religion, or prohibiting the free exercise thereof." It says nothing about the Separation of Church and State.
The words "Under God" are In the Pledge of Allegiance
James Madison, The Chief Architect of the Constitution once said,
"We have staked the whole future of American civilization, not upon the power of government, far from it. We have staked the future of all of our political institutions upon the capacity of each and all of us to govern ourselves ... According to the Ten Commandments of God."
Are you so sure that we are not a Christian Nation?
The separation of church and state was cautioned against by Thomas Jefferson in a letter to the Danbury Baptist Association. The Constitution says that the government shall not favor one religion over any other, and that to be elected to office of any kind, no religious doctirne is necessary. Nowhere in the Constitution is the phrase seperation of Church and State used.