Everson v. Board of Education applied the establishment clause of the 1st amendment to state law.
Applying the Bill of Rights to state law is known as incorporation as in, incorporating the Bill of Rights to the states. It has had some controversy as reflected in U.S. Supreme Court decisions as to how, which and when specific amendments are or were incorporated. The most recent incorporation came in McDonald v. Chicago in 2010. There are those who argue that the 14th amendment was designed to incorporate the first 8 amendments. Others have attempted to argue, even as late as that 2010 case, that not all amendments are incorporated against state law.
In Everson v. Board of Education, the Supreme Court wrote:
"The 'establishment of religion' clause of the First Amendment means at least this: Neither a state nor the Federal Government can set up a church. Neither can pass laws which aid one religion, aid all religions or prefer one religion over another. Neither can force nor influence a person to go to or to remain away from church against his will or force him to profess a belief or disbelief in any religion. No person can be punished for entertaining or professing religious beliefs or disbeliefs, for church attendance or non-attendance. No tax in any amount, large or small, can be levied to support any religious activities or institutions, whatever they may be called, or whatever form they may adopt to teach or practice religion. Neither a state nor the Federal Government can, openly or secretly, participate in the affairs of any religious organizations or groups and vice versa. In the words of Jefferson, the clause against establishment of religion by law was intended to erect 'a wall of separation between Church and State.'" 330 U.S. 1, 15-16.
All justices, in this decision, agreed that the 1st amendment was incorporated against the states. They disagreed whether or not that incorporation should result in striking down the question that was before the court (whether the state could pay for school buses to take children to religious based private schools.) In the end, it was a 5-4 decision that the states could pay for transportation.