First amendment, extended by the fourteenth, says that a State cannot abridge free speech, religion, etc. . You can't fire a state employee, therefore, for something he/she says away from the workplace, or for his/her religion. A private employer, constitutionally, could fire someone for saying something the employer didn't like, or for his religion. 14th amendement says the state must give citizens equal protection of the law; again, this prevents 'at will' firing. The Bill of Rights also requires due process (which goes back to the Magna Carta: see http://caselaw.lp.findlaw.com/data/constitution/amendment05/11.html)
Perhaps you fail to understand the market participant doctrine, that says a state is not bound by those same constrains when it is operating in the marketplace. In this case, in the eyes of the law and that doctrine, it is operating as an 'employer' not a 'state'.