First, E. J. Dionne writes about disagreements within the conference of bishops. He reminds us that the vast majority of bishops have not entered into these lawsuits and that many feel they are politically motivated, participating in Republican attacks on the president.
Cardinal Wuerl writes an op-ed explaining his position in suing the administration. The essence of the argument is that the government is definining what is and isn't religious and that that should be left to religious bodies.
This seems like a red herring to me. Let me explain.
The United States has long (for one hundred years) been debating how to improve health care access. It was a major part of the discussion and debate in the 2008 presidential election. This led to the Affordable Care Act, passed by the elected representatives of the American people (even if many of us find the final bill flawed and lacking in the broad scope and radical change we had sought).
As part of that decision, we collectively chose that women had a right to access to contraception. Since our current (still deeply flawed) system is for health care to be provided by employers rather than a single socially supported system, that meant employer-based health insurance systems would have to provide for this right.
This raises issues for religious-based employers, so it was left to the Department of Health and Human Services to decide where to draw the line in what is clearly a gray area. And that is what the Department did. You can disagree with how the line was drawn and advocate for a change, that makes sense, but the cardinal's language is overwrought.
The "government" (he sounds like Grover Norquist when he uses the word) is not deciding what is and is not religious. The Dept. of HHS was making a policy decision of how to apply the religious exemption. The department is not saying that schools and hospitals and social service agencies are not "religious," only that they do not qualify for the religious exemption from providing this right to their employees. Government agencies and courts do make these sorts of decisions all the time, and it is not anything radically new. There are also clearly established constitutional and legal guidelines for adjudicating these things (for example, if there is a "compelling interest," we can do something that violates religious conscience or practice).
And one more point, which I've made before, all of us end up participating in systems and contributing funds to things that violate our consciences. I believe in non-violence. My taxes support wars that I believe are immoral. I cannot seek to opt out of this, nor should I. And, interestingly, the Roman Catholic Church holds similar positions on war and violence, but you don't hear them making these objections anywhere nearly as big an issue as being told that they must provide what the larger society feels is a right of women's health.