You don’t understand how medicine works.

A doctor can’t just decide to start doing a new medical procedure. They need to learn and practice. It takes a significant investment. And to be good at a procedure requires doing it often.

Even my dentist referred me to another dentist for a relatively simple procedure, because the other dentist is better at it and does it more often.

For a doctor that is not experienced in performing abortions, doing an abortion would be medical malpractice. If anything goes wrong, and the chance is higher due to lack of experience, they will be sued and they will lose the tort case.

So doctors have to choose what procedures they specialize in. And obviously, nobody who is morally opposed to performing abortions will choose to specialize in performing abortions.

It is a conscious choice and long term commitment to be an abortion providing doctor.

Not performing a procedure that you don’t regularly perform is prioritizing patient health.

Right, because you would want to be the patient to undergo a procedure by a doctor that never performs that procedure?

No sane country does this.

Maybe go live in a dictatorship if you like to force people to cut into other people’s bodies.

A hospital is just a building and the organization that owns the building.

The real question is, should hospitals be allowed to force or forbid doctors from providing medical care?

A doctor (Catholic or not) should never, and can never, be forced to perform a medical procedure, including abortions. And they also shouldn’t be forbidden from performing a medical procedure.

Hospitals just provide rooms and equipment so that doctors can provide the care that their patients need, within their ability to provide that care.