Well, let me take a step to the side here. As I have been in private practice now for several years I can shed some light here...
First, be aware that most tier1 residency programs will not take a student who is already talking about what they will and will not do, particularly when it comes to contraception. That's just life. Quote the law if you want, you just won't get in. Now, since we are talking about Catholic hospitals that will not likely be an issue as they are generally smaller programs and less desirable.
Second, it will strain your relationship with other residents and fellows because of how it will cause workloads to shift. When you refuse to help a patient and it must then get bounced to another resident, they will not be happy.
Third, consider what happens after residency. Who will hire an OB/GYN who refuses to do all sorts of things? Sure, the abortion thing is not an issue there, not at all. However the tubals? That's annoying. The contraception? That's unemployment. A huge number of patients request contraceptives and if you refuse to offer them they will find another physician who will.
This is your big problem. If you are in a private practice they won't hire you because this will cost the practice money. If you are in your own practice this will cost you even more money. If you are an employed position it will last for a bit longer, but most of their models are also revenue driven and you are now alienating a huge portion of your patient population.
So, my conclusion is this.
You can do whatever you want, no one will legally force you to do anything. You will however kneecap your career before it starts. It will severely impair your ability to join a private practice, it will completely eliminate your ability to run your own practice, and it will impact your earnings as an employed physician.
So either way, if this is your viewpoint then my suggestion would be that you need to consider another specialty. You are walking into a business model like an academic. Physicians don't operate in a vacuum, you simply cannot throw away such a huge number of customers and expect to be employed or make any money.