"Any private hospital, Catholic or otherwise, that has religious or moral objections should close their OB/GYN clinics, and maybe even their ER doors. But if this happens on a large enough scale, I can see a scenario where the state government tries to take over those hospitals "for the public good."
Both ER's and OB/GYN sections are often money-losers. If the states want to take over those functions "for the public good", I suspect that more than a few hospitals will be more than happy to hand them over.
In my personal view, I think the western Catholic church should be getting out of the hospital business, at least in the U.S. As compared to other countries, we are not "medically underserved". The reason why Catholic hospitals were created in the first place was to serve poor immigrant Catholics who had no other place to turn. That problem has largely been eliminated if for no other reason than American Catholics are by and large more affluent than they were 100 years ago. As I pointed out in a previous post, you don't have to be the one who actually provides a service to ensure that the service is provided.
There is risk in any strategy a Catholic organization takes to stay true to the faith, and expropriation is one of them. I don't think expropriation is a particularly high-risk in this instance.