The Catholic Church in America is a tax free business with much of it's capital invested in hospitals and other medical facilities.
Since Medicare and Medicaid have rules that all vendors must follow it is logical that if they wish to do business and receive federal funds they must in fact comply. They can not change the rules nor make their own. If in fact, they refuse to comply they should lose all Medicare and Medicaid eligibility.
Catholic hospitals care for all religious sects, what right have they to enforce their views onto others. If they are operating as a business they should and must observe the mandate dictated by law and the rules for receiving public funds.
If in fact they do not like the rules they have the choice to privatize and use their money(funded by donations from their faithful). If they try that route they will see how much of a majority they will retain.
It is quite easy to say "they should not have to follow that rule because it is against their religious beliefs" but money talks.
Again, if a woman's right to choose is not protected then the tenants of the constitution will not be for all the people.
They will become third class citizens, second to men and third to a fetus. Women have rights and if your religion says it is wrong at least then the woman has the right to choose wrong, thus proving she is in fact human, with rights.