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.