It's virtually a non-issue. I don't claim to know the answer to the conflict, but I do have serious reservations about one denomination imposing its dogma on people who are not members of that denomination, be it by economic means or otherwise. Of course, since comprehensive health care is not considered a basic right of all residents (or even citizens) of the US, it gets even more complicated.
However, and I say it again, imposing Catholic dogma on non-Catholics does not strike me as "religious freedom" by any stretch of the imagination - unless you are a Catholic.
It would be interesting to know how many Catholic women use "The Pill". I would be willing to bet that damn close to 50% do. The ban on contraception does not have a lot of adherents in the pews, no matter what comes from the pulpit.
Here are some of the Catholic leaders' comments (http://mediamatters.org/research/201202130008):
University Of Notre Dame President: "We Applaud The Willingness Of The Administration To Work With Religious Organizations To Find A Solution Acceptable To All Parties."
Association Of Jesuit Colleges And Universities "Appreciates The Compromise That President Obama Has Made To Accommodate Religious Institutions In Regard To The Birth Control Mandate."
Catholic Charities USA "Welcomes" The Obama Administration's Accommodation Of Religious Institutions As A "Step In The Right Direction."
Catholics United "Supports Obama Administration's New Compromise Regulation On HHS Contraception Rule."