A classic example of how the Constitution works is illustrated by the difference between a public and a private school. A public school is a governmental entity and, therefore, is prohibited from restricting the free exercise of religion. On the other hand, a private school can promote or proselytize in religious matters without any governmental interference, and no matter how offensive the promotion or establishment of a religion may be to an individual, the First Amendment has no application to a private school. A private Christian school can require mandatory chapel every day and may also prohibit the distribution o f religious literature. However, a public school would violate the Establishment Clause by requiring mandatory chapel every day and would violate the Free Exercise and Free Speech Clauses by prohibiting the distribution of religious literature. A public school could not compel a Jehovah's Witness to salute the flag because to do so would violate the student's free exercise of religion. A private Christian school could compel a student to salute the flag.
(Mathew D. Staver, Eternal Vigilance: Knowing And Protecting Your Religious Freedom
, pg. 31)