The hospital is free to give up it's state issued license to operate.
And the other patients it serves? What about them? Why should they be forced to close rather than exercise their freedom of religion? Do you think a private or parochial school should be forced to teach homosexuality is an acceptable alternate lifestyle? Or that a Baptish crisis pregnancy center must refer unwed mothers to abortion agencies? Or that a Jewish day care center must serve pork chop if requested to by non Jewish parents?
The only reason for the law is hostility to the Catholic faith. The morning after pill can be made available by other institutions which do not have to compromise their faith to do so.
That would be the license that wasn't required before 1900 right?