Establishment Clause

Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof... The Establishment Clause is a clause in the First Amendment to the United States Constitution that states that the US Congress cannot establish a state religion. The Fourteenth Amendment has long been recognized as extending that limitation onto the legislatures of the individual states.

The Establishment Clause prevents government at any level from demonstrating any preferences toward religion. This means no preferences for a single religion, or for religion as opposed to secularism. This is why government institutions (such as public schools) cannot support religious causes — or interfere with expression of religious sentiment by non-government authorities.

Treatment by fundies
There are, however, people who believe in a more literal interpretation of the Establishment Clause. They argue that the clause only prohibits Congress from establishing an official church, but that the government can openly favor one or more religions over others. The courts tend not to agree.

Others have gone so far as to claim that the authors of the Bill of Rights only wanted to prohibit the establishment of a particular sect of Christianity at the Federal level, at the expense of the others, and that the Founding Fathers always intended for the government to be non-denominationally Christian. These claims are based on some very strained readings of certain select letters and articles written by Washington/Jefferson/Hamilton etc., and are directly contradicted by other letters and articles written by the same people.