The answer is: it depends.
A Catholic cannot directly participate in abortion. However the principle of material cooperation would appear to permit a Catholic to hold a position in a general hospital that also might perform abortion so long as the Catholic never participates in any particular abortion.
The basic principles for not being morally responsible for cooperation with an immoral action are:
- The action of the person must be intrinsically good or neutral
- The intention of the person has to be good, not only must he not desire/intend the immoral action of the other but he also must not be seeking any other illicit intention
- There must be a legitimate and proportionate reason for the action
- All willed good intentions cannot result from the immoral action
The position held by the Catholic at the hospital must not directly be involved in an immoral medical action.
The Catholic individual must not desire to further immoral medical actions by taking the position.
The Catholic must have a legitimate reason for taking the job. If someone only works with heart patients, that is a good intention since lives are being saved. If someone simply needs a job and takes a job in the billing department, it is also a good intention since we need to provide for our families.
All moral medical/health activity cannot be the result of the immoral medical activity. On this principle a Catholic would be morally prohibited from working any job (even janitor) for a health center whose primary focus or source of income is immoral medical activity since all other legitimate medical activity would then flow from the immoral activity.