While the heated reaction against the HHS mandate is now nothing new, the responses from Catholics and their reasonable friends have not all been the same. Christopher Tollefsen at Public Discourse has helpfully outlined and explained each of what he opines are six different (though not competing) reactions against the mandate. The final response, probably most well-known, can serve as an introduction to those still unfamiliar with the problems that the mandate brings to bear:
The final consideration is one that required no such anticipation, and is best understood, I think, as a consideration of religious liberty. For among the most stringent duties of Catholic institutions in providing witness is one which is well publicized, and was in effect before the mandate was ever under consideration: that they in no way undertake to make available drugs or procedures held by the Catholic Church to be morally abhorrent, while carrying out the other central features of their mission. This judgment is a judgment of Catholic policy. And it is a policy judgment the making of which is both necessary and central to the Catholic identity of a religious hospital or university. Necessary, because a Catholic apostolate is constituted by its moral judgments and choicesby its judgments and acts of conscience. Without the opportunity to make judgments and act in accordance with its conscience, there can be no institutional reality or identity at all. Central, because no institution is Catholic unless its judgments of conscience are those of the Church.
Read the other five responses here