I have written recent posts on religious discrimination. Employment decisions can be based on religion in some circumstances.
First, the restrictions under federal law only apply to employers with fifteen or more employees (state law may have similar protections but require fewer employees).
Second, there may be a BFOQ, a bona fide occupational qualification. For instance, a Catholic church is not required to consider the application of a Baptist minister to be a priest. Certain religious belief may also be a qualification when the job involves teaching or presenting doctrine. For example, a private, religious school may lawfully require that its teachers be members of a particular denomination, and may bar anyone who is not a member from employment. BFOQs apply when the qualification is reasonably necessary to perform job duties for a position or when necessary to the normal operations of the employer. A Christian college may lawfully require positions such as president, chaplain, and faculty to be Christians or to make a profession of faith.
This exception also applies to the other protected classes under Title VII, as well as to the protections under the ADEA. For example, a transportation company may legitimately place an age restriction on a pilot or driver for public safety purposes. And a “gentlemen’s club” need only hire women for some of its positions because being female is essential to “the job.”