Hospitals tend to be profitable, religious affiliated or otherwise. Religion, aside from some seventh day adventist institutions, tends to be more veneer. Business CEOs and doctors gone over to business run them, not actual nuns or religious leaders.
It would be highly unusual for an urban hospital, in an area where doctors want to live and work, to go out of business. Medicine is contingent on location, locations where doctors want to live and work. For hospitals, that means specialists and surgeons, because that’s where the money is.
The loss leader of medicine is mother baby, and NICU. The latter are commonly referred to a million dollar babies, and that was well before 2020 inflation happened. Birth centers exist in the red, which is why not every hospital has one. Surgeons in other areas earn the money to support a birth center. That gastric bypass? That open heart surgery? Paying for mother baby to stay open.
When hospitals close birth centers or rural locations it’s not about religion, it’s straight up income stream based on earning doctors at that location, or how capable the city location is at covering the rural location while still maintaining profit.
Non-profit is a tax status that isn’t what it sounds like. There is always profit for a hospital or it would be closed.