Can I just say this is unmitigated bullshit of the highest order and end the argument there? No, I guess not.
First off, and lets be clear about this, this issue has already been litigated to the highest court and the Churches have lost. See, many states already require insurance to cover contraceptives (and here we're talking about that scourge of modern society, the pill, not something like free condoms if you show your insurance card). And the Churches (well, some of the more loony-right winged churches) cried foul and said, "We'll sue!" And they all lost. Every single one of them.
Why? Because the law doesn't mandate that they use birth control, they're not being singled out for special provisions, and not everyone who works for those organizations is actually a member of the said religion. Also (and we'll get back to this), they accept government money (your tax dollars) to run their charities (thank you G. W. Bush), fix and repair their buildings (again, since GW), and Medicare, Medicaid, and both direct payments to hospitals and partial block grants (state distributed federal money). And, again, for the church offices, employees, etc, you have an exemption. It's only when you run an outside business that you need to comply with the law.
So first, a little thing about the compromise. President Obama basically went to the insurance companies and said, "Hey, what I want you to do is cover the birth control prescriptions for free, and not include that in whatever you bill these church affiliated (and sometimes not much more affiliated than with a name or address) business." And the insurance companies went, "Wait, you want us to cover the pill, the thing that lowers out costs (and price), that essentially costs us less than $10 a month, AND we get to bill them like we weren't including that (which is a higher amount)? Fuck yeah!" See, health insurance companies cover the pill, vasectomies, tubal ligation, hysterectomies, etc, because they are much cheaper than even a non-complicated pregnancy (also, see notes about how we're waiting much longer to have babies, which adds to the complexity of the pregnancy, which adds to the costs). So they see it as both reducing their costs for those pregnancies and then the added costs of the pediatrics (which are normally discounted to the end user). When you specifically request to not have those services covered, your potential use and cost goes up, and then so does your premiums (insurance is all about covering the spread).
But now that compromise isn't enough. It's a classic case of moving the goal posts. Also, I'll note here, that while the Catholic Church is against all forms of birth control (except the rhythm method or abstinence), 85% of Catholic women have used the pill (I couldn't find a stat on condom use). Now it's "we don't want anybody using the pill, and because it's our 'religious freedom' we want to make sure the rest of you don't have the choice either." Or, "You can have your religious freedom all you want, as long as it conforms to the most conservative Catholic or Evangelical faiths, and you must belong to one of them."
That's right, what the Churches want is the freedom to enforce their religious precepts on everybody else. Protestant? Agnostic/Atheist? Buddhist, Hindi, Vodun, whatever… domani, domani, domani, you're all Catholics now. That's what this is about.
See, if it was about "religious freedom" those very same people would say, "We don't want your government money." What's that? You don't hear them talking about how they'll leave all that juicy, juicy tax money behind so that they can remain pure to their faith?
And here I will point out the the very same people who cry that religions can separate their mission money from their church funds and that the two aren't related are also the ones who talk about how even with Planned Parenthood having separate bank accounts and business structures (and in some countries, having completely separate corporate identities sharing facilities) that you can't really separate out those funds because any money that goes to the good will and health services also free up funds/help pay the rent of the abortion side of businesses.
So, that's fine. You want to keep your "religious freedom" to enforce your will on people who aren't of your faith? Stop taking government money.
Also notice they're not decrying coverage for those other medical procedures (vasectomy, etc), or coverage for viagra, or really any of the other things that also violate their "religious freedoms" (well, they don't see it that way, because they benefit men), just abortion and the pill. Because they want a government that gets out of your personal business, doesn't get between you and your doctor (and God), and is a government that's smaller. Just small enough to fit inside women's uteruses (see also Personhood Bills)
So, that this is about "religious freedom" is a bunch of bull. This is about keeping power over women by regulating their reproduction. This is about not wanting to live in modern society because it's all icky and people have to share. It's about convincing you that some people are more equal than others.