With few exceptions, American colleges have become partners with the federal government. At the university level, Uncle Sam provides large grants for research and service. For the smaller colleges driven by tuition, the federal government guarantees the students' loans and now often originates those loans. Thus, the federal government is now the lender whose loan terms determine where students may attend college. (E.g., one can get a student loan to study religion at a state university but not to study for the priesthood.)
The clash we are now seeing is between the First Amendment rights of religious organizations and colleges and Fourteenth Amendment rights as trending for the formalization of same-sex partnerships. There is a ton written on this, and it will get much more attention for the foreseeable future, e.g., Gay Rights, Religious Freedom, and the Law, Religious Freedom v. Gay Rights Debate, Catholic-Jewish divide on Supreme Court, and Becket Fund's "score card" regarding the HHS mandate.
My own college, Gordon College, received national publicity because its president signed a letter to President Obama asking for exemption from an executive order against discrimination based upon sexual relationships. Gordon College is a private school that has retained its traditional Christian understanding of sexuality and marriage, and faculty and dorm supervisors as well as students sign a statement of faith and conduct acknowledging the college's position and agreeing to abide by it. The college would not hire a faculty member cohabitating with either a man or a woman. The letter caused a fire storm in higher education in New England. More here: Inside Higher Ed, Huffington Post, Boston Globe, First Things, National Review, Washington Times, and Christianity Today.
The secularizing forces in our country want to require the colleges receiving federal financial aid funds to abide by all regulations applying to corporations doing business with the federal government. As seen in the dissent in the Hobby Lobby decision last year, this segment of our culture sees little room for a corporation, non-profit or for-profit, to exercise judgment based upon the religious convictions of its board of directors. Nonetheless, recent court decisions have favored both of the two groups that are clashing: religious organizations (and religious practitioners within corporations) and gay advocates.