I took a deep dive into the subject of Catholic hospitals and health care in the United States a couple years ago for a story I was working on.
What's particularly crazy about the situation of Catholic hospitals denying care based on religious principles (And it's not just abortion; talk to trans people about their frustration trying to access health care in communities dominated by Catholic healthcare systems.) is that Catholic hospitals aren't in any meaningful sense actually Catholic.
1.) Medical staff at Catholic hospitals are no more likely to be practicing Catholics than staff at other hospitals. Ditto for other staff like administrators, social workers, maintenance staff, etc.
2.) Patients at Catholic hospitals are no more likely to be practicing Catholics than patients at any other hospital.
3.) Funding for Catholic hospitals is almost identical to funding for non-Catholic hospitals, meaning revenue comes from private insurance companies and the US and state governments in the form of Medicare and Medicaid payments. Catholic hospitals in the United States do not receive significant operating revenue from the Catholic Church or from donations by Catholic people.
So if medical services aren't being performed by Catholics, particularly for Catholics, or paid for by Catholics, we're left asking what the point is of allowing the Catholic Church to control hospitals, especially when they ration care based on sectarian religious ideas.
When you consider that in some parts of the United States Catholic hospital networks offer the only geographically convenient access to healthcare for significant numbers of people, the question becomes pretty important.