Civil rights are of paramount importance in our society. These cannot be maintained if entities of public accommodation- which does include privately owned businesses like restaurants, retail establishments, and hospitals- are allowed to discriminate. This was one of the major reasons for the Civil Rights Act of 1964, which was enacted to protect the EQUAL rights of all individuals in our society.
Let me begin by saying that I am only addressing public entities, not private ones. Even a liberal like me respects the right of private entities to discriminate. Anywhoo: hospitals, and other public entities do not have the right to discriminate because their purpose is to serve the public. This is especially true if they receive public funding. Religious entities who wish to receive public funding are in mind as I right this. Let me know if I should clarify anything.