UPDATE: Just which Catholic institutions are "mandated" to provide contraception? Not EWTN
A new lawsuit against the government regarding the HHS mandate adds a new wrinkle: The Catholic TV network EWTN Global is suing the feds , seeking to have the rule declared unconstitutional. I'm wondering if they could have saved some money by actually applying for the exemption in August 2013, when the rule goes into effect. EWTN is a purely sectarian enterprise; I'm not sure how it's incorporated now, but it used to be owned by Mother Angelica's religious community, and it is almost certainly a non-profit incorporated for religious purposes: Since they have a primarily religous purpose and employ and serve mostly Catholics, I think they'd have a good shot at an exemption.
This lawsuit is to me another sign that some of this outcry is purely political in motivation. Why not apply for an exemption, then sue if denied? I think Catholic orgs and the bishops are on dangerous ground here. It is one thing to assert free exercise; it is another to appear to be choosing sides in an election year.
ORIGINAL POST: Not to beat a dead horse, but given all the volume the U.S. bishops and Catholic journalists (such as the editors of Commonweal  and E.J. Dionne ) are giving to this issue, it's worth parsing just who is being "forced" to pay for the Pill. I don't think anyone is paying attention to how complex the issue is, especially the definition of a "Catholic" institution. All "Catholic" institutions are not created equally, legally or even canonically speaking.
The HHS rule exempts religious institutions that primarily employ and/or serve their own members. So I think it's safe to assume that the following Catholic institutions are exempt:
1. Catholic parishes and parish schools: This seems somewhat obvious. Even if some parish schools serve significant groups of non-Catholics, their purpose is primarily education in a Catholic environment, and most of their teachers and administrators are probably Catholic, at least in most cases.
2. Diocesan agencies directly connected to the bishop: the Catholic newspaper, for example, the office of education and communication. Here in Chicago, that's a large group of people. I'd include diocesan and other seminaries in this, since they by and large employ and enroll Catholics only. I'd also extend this to the U.S. Conference of Bishops and its staff.
3. Religious congregations (Sisters of Mercy, Jesuits) and the agencies over which they have direct control and ownership: Again, somewhat obvious. The Claretian Missionaries, who publish U.S. Catholic, have publications, a shrine to St. Jude, various other ministries, that primarily serve and employ Catholics. I'm sure the St. Jude League (our parent company) and Claretian Publications would qualify for the exemption. It might also include some hospitals and universities (see below).
4. Most Catholic high schools, whether diocesan or religious, for the same reason as most parish schools would qualify. They may educate non-Catholic students, but they have a primary religious function--Catholic religious education and spirituality are required components.
Now some gray area: What about Catholic Charities?
Most (maybe all?) Catholic Charities agencies are separately incorporated in dioceses. So it's "Catholic Charities of the Archdiocese of Chicago." But--and this is an important but--most Catholic Charities agencies are not part of the diocesan legal structure. In other words, Catholic Charities is a separately incorporated social service agency connected to the local church "aspirationally" but not directly funded by it necessarily. In fact most of Catholic Charities budget comes from public sources (state and federal).
Since Catholic Charities doesn't necessarily primarily employ Catholics or primarily serve them, I suspect they would not qualify for a religious exemption to the HHS rule, but because of their particular connection to the local church, they may have an argument for the exemption. For example, the archbishop of Chicago appoints all the board members of Catholic Charities in this diocese.
Then there's the Catholic hospitals and universities. This is a much harder sell. Most Catholic hospitals and universities were founded by religious communities that long ago gave up direct ownership of them. Some are large non-profit corporations (hospitals), others are controlled and governed by boards of trustees (universities). It seems possible that some Catholic colleges could argue that they have a primary religious purpose, such as Franciscan University in Steubenville, but others, such as Chicago's enormous DePaul University, probaby would not. Notre Dame President John Jenkins has made a big deal out of this, which would lead one to believe that he thinks ND should be exempt. But it seems a hard sell to say that a faculty member of the ND law school or a member of the janitorial staff must comply with church teaching on birth control.
Which goes to an important question: How will the rule be interpreted? I suspect it could be interpreted rather generously in the case of smaller religious colleges, less so for hospital organizations (Catholic Health Association's statement here ), whose connection to the local church (diocese) is far more historical and aspirational than it once was. Then there is the issue of public funding ; my suspicion is that, the more an institutional budget relies on public money, the more the attached strings will apply. Institutions will have to apply for a waiver--unless they just assume they have one and then have to litigate it if an employee sues--and HHS will have to decide who qualifies and who doesn’t. That's why I think the Supreme Court will most likely strike the rule down, because a government agency will be in a position of determining whether an agency is religious “enough” or not.
Either way, I think this is way more complicated than the bishops are making this out to be ; one wonders, as Kevin Clarke does at America,  what is motivating it. By and large, bishops as employers will not be affected, since few have diocesan hospitals, though there are a few diocesan universities. So I don't know what to make of several bishops' refusal to obey the HHS mandate--as employers, many will probably be exempt.