Debates on this issue have made liberal use of the term "religious liberty," a term deriving from the First Amendment to the Constitution. But the religion clauses of that Amendment have two parts: the "free exercise clause" and the "establishment clause." Unfortunately, many of the discussions on the issue have given the impression that the religious liberty at issue is the sole province of the Catholic Church. This relegates of the rights of women as somehow outside the realm of the religion clauses.
"Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof..."
Civil libertarian groups, such as Americans United for Separation of Church & State, and the Religious Action Center for Reform Judaism, argue - using the history of the debates creating the religion clauses - that the wording prohibits any government action that could be interpreted as touching upon an establishment of religion. This would include enacting a preference for any particular religion, as well as for religion over no religion.
In this case, the rights of conscience apply to employees of Catholic Universities and Hospitals, as well as to the Catholic Church. The Obama Administration's action avoids having the dictates of the Church imposed upon these individual women - which leads to the other distinction being glossed over.
During my days as a church-state activist, the term "pervasively sectarian" was used to distinguish between an actual church, which is allowed to discriminate in hiring and enforce its religious dictates, and an affiliated entity - such as Catholic Charities, or a Catholic hospital or university, which cannot be discriminatory. The Obama Administration rule explicitly exempts pervasively sectarian organizations such as churches from this rule. But hospitals and universities are made up of people from all faiths, and therefore, cannot impose Catholic teaching on their employees. Discussions of this controversy that I have heard, have used general terminology in passing, without mentioning the history of the "pervasively sectarian" concept in church-state history.
I think the distinction the Obama Administration has made between actual churches and other Catholic institutions strikes the right balance.