First, I will say that religious institutions (e.g. churches, mosques, synagogues, other places of worship, seminaries, etc) do have exemptions from the laws that secular non-profits don't have.
Religious organizations can discriminate on the basis of religion in hiring and firing. In areas where sexual orientation non-discrimination laws are present, religious organizations are exempt from following these laws as well. They can discriminate on the basis of gender in their hiring. In other words, they get to do a lot of things that would be illegal and wrong if a secular business were to do them.
But this exemption from secular law should not apply when a religious body operates a secular business like a hospital or a school.
These secular businesses employ members of all faith traditions and even those who are non-believers. The same is true for their clientele - they may belong to other faiths or have no faith at all.
Basically, we're talking about hospitals and colleges that have religious decorations on the walls and statues in the lobby. These trappings should not give a hospital or school "special rights" to ignore laws that secular non-profit and secular for-profit corporations must follow.