the problem with your argument is that once you upon up a hole like this, health care providers can then refuse to stop carrying products or services based on religious views. what if a catholic hospital refuses to admit a gay patient because they disagree with his/her lifestyle? what if a religious hospital refuses to admit an aids patient because AIDS (in their eyes) is a disease created to punish gays. what if a rape victim is brought by ambulance to a religious controlled hospital and that hospital refuses to carry emergency contraception.
this opens up a huge can of worms, and it actually a great argument for a single payer systems where everyone has access to the same care and services, while everyone pays the same price.
Health Care providers (such as Catholic hospitals) already don't provide certain services that go against their religious beliefs, for example they would not do a tubal ligation on a woman after she delivers a baby, if she wanted one. However, Catholic hospitals would not turn away a gay patient, because even though they may disagree with that person's lifestyle, they are still in need of care, they are still a human being who needs medical services. Would they provide medical services that went against what the Catholic Church teaches? No. But they definitely treat people who are gay, or who don't even believe in God or are even anti Catholic. This is basically an argument for freedom of religion.
As for your rape scenario I'm sure it happens already. Because I know for a fact Catholic hospitals do not and will not do anything to cause an abortion etc...they will treat the rape victim but if they want something to make sure they don't end up pregnant they have to go somewhere else.
Now you may not agree with it, but a Catholic owned hospital should not be forced to do something that goes against it's freedom of religion. That opens up a whole can of worms in itself. Don't you think?