Known as the Warren Court, this period is known as the period Earl Warren served as Chief Justice of the US Supreme Court (from 1953 to 1969). It was an Activist Court that expanded individual rights and power of the federal government to enforce civil rights legislation.
One example that the Warren Court expanded the First Amendment was the expansion of Freedom of Religion. In the case Sherbert v. Verner in 1963 the Supreme Court decided that if an employee can prove their religious conflicts they are protected by law from discrimination. In the case Engel v. Vitale in 1962 the Court ruled that it was illegal for states to require official school prayers to be recited by students and in Abington Township School District v. Schempp in 1963, the Court ruled that school-sponsored Bible readings were unconstitutional.