On January 11, the Supreme Court ruled unanimously in the Hosanna-Tabor Case that a "ministerial exception" is grounded in the First Amendment, and that a teacher fired at Lutheran school was lawfully fired according to that exception and that she cannot sue
Ministerial exceptions in hiring and firing illustrate one margin where religious and other rights can come into conflict. For example, hiring based on religious characteristics is certainly a form of discrimination, but the Supreme Court acknowledges that such discrimination is legitimate for ministerial positions. Importantly, this ministerial exception, as interpreted and articulated as part of this ruling, applies to religious institutions and their ability to provide religious services. The institution is free "to accept or retain an unwanted minister."
See some useful analysis from the Religion Clause blog here and here.