Private schools (those which receive absolutely no money from any government entity or foundation) can discriminate in anything that they do. A good example is Bob Jones University, a highly religious private institution.
Although they have gotten rid of their racial discrimination, which lasted from 1927 to the 80's, due to tax status reasons [see 461 U.S. 574 (1983)], they still discriminate based on gender, sexual orientation, and religion. [see their nondiscrimination policy at:
http://www.bju.edu/admissions/nondiscrim.html
Basically, private schools can do what they want to do.
Similarily, churches can discriminate their hiring practices to those who are church members without getting in trouble.