The Hitch
The hitch in your argument is that some of the religious institutions receive federal money. If they want to take the high road and discriminate against people who believe differently then they should not take any federal money and rely on their own income streams. The federal government is not supposed to support or oppose any religion although that is the theory and not always the practice.
Rush and the contraceptive issue shows that the surface of this is religious freedom based but the real core is about sex and how to control sex. I am surprised that Rush has not been taken to task for muddling the religious freedom argument.