what makes you think that a catholic bishop is more moral than a woman seeking an abortion: a choice she is permitted to make for herself in law; it is not a choice that a bishop makes for her. indeed, it is a dilemma he will never even face.
if the catholics wish to get into healthcare, that's fine. but they shouldn't get to impose their idea of right and wrong upon their patients. as a professed libertarian, i am astonished you would think otherwise.
what you are describing is the value system that permitted racism over the use of drinking fountains. if the person providing the fountain thinks black lips contaminate the fountain, he has a right to stop that person using it.
but the law protects and defends the rights of of blacks and the rights of women in circumstances in which some group is prejudiced against them. as it should.
i care not a jot for a mitre and sceptre. you do healthcare, you provide the services the law says you must. if you do not wish to, try a different business. like conducting religious services.