The same as any other doctor's:
“Conscience,” or personal beliefs, was …. used to deny care to HIV/AIDS patients. I started practice well before HIV-AIDS was recognized, when little was known about its transmission. I clearly recall the struggles both of patients and of health care workers who wanted to refuse to provide care to AIDs patients—either because of their religious beliefs or because of their own fears of becoming ill. Despite these concerns, it was demanded that health care workers care for all, and put the patients’ needs first.
… Catholic hospitals provide 20-30% of the hospital care in the United States.Religious health systems received more than $45 billion in public, taxpayer-supported, funds, including Medicare and Medicaid funding. The Catholic Health Association, for example, also receives huge tax breaks as a “non-profit, charitable” organization. Thus, religiously-affiliated health systems have an enormous influence on health care, especially in rural areas, where they are often the sole provider.