According to the U.S. Equal Employment Opportunity Commission, it is illegal to discriminate against a current employee or candidate based on race, color, religion, sex (including gender identity, sexual orientation, and pregnancy), national origin, age (40 or older), disability or genetic information.
Does this apply to religious institutions selecting their own clergy? I'm going to guess that it's allowed if there is a religions reason (e.g. the Roman Catholic church has a religious restriction forbidding women from being priests). But if there is not a religious reason, would they be permitted to discriminate?
For instance, could a Protestant church that does not have any religious restriction regarding the race of clergy still choose to discriminate based on race for their own reasons (perhaps they only want to hire a black pastor, or say that they will reject candidates who are black pastors)?
Or are religious institutions given some sort of protection regarding their hiring practices?