This is, of course, a very controversial matter. There is no objectively correct answer. Let us look at both sides of the issue.
On the one hand, we can argue that hospitals should be able to refuse to provide abortion services. Since many people are morally opposed to abortion, they should not have to participate in providing it. Doctors should not be forced to perform abortions. Support staff such as receptionists should not be forced to help facilitate abortions. This would be as abhorrent, for example, as requiring a Jew to eat pork.
On the other hand, we can say that abortion is not a matter for anyone other than the pregnant woman to decide. We can argue that abortion is a woman’s right and no one has the right to take that right from her. In this view, allowing hospitals to refuse to provide abortions would be morally tantamount to allowing them to refuse to treat African American patients.
My own view is that hospitals should be allowed to decline to provide abortions. However, the government should also not put barriers in the way of providers who do want to provide abortions. That way, people with different views could be able to stay true to their own consciences.