This is, unsurprisingly, attested to by the Constitution. I previously cited the first amendment, which out of context presents requirements apparently paradoxically at odds with the rule of law, namely an idea that religion deserves some special protection. However, in context and especially considering the tenth amendment there is no paradox, but rather a liberty specially named because of historical (and, at the time of America's founding, ongoing) assaults on that liberty. That tenth amendment says,
The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.
The ninth amendment similarly makes the point that rights - that is, liberties - are more general than enumerated solely in the Constitution: that, in general, the government does not have the right to disestablish our natural or human rights. I am on the side which believes that this indicates that governments - especially our constitutional one with its explicitly stated limits - should impose as few restrictions as possible.
It is not a coincidence that today the religious groups who are protesting that their rights are being violated by this new executive mandate are in general on the same side of politics which has been protesting for years that commercial and civil liberties have been violated: by excessive taxation, prejudicial government policies, oppressive regulations, and the like. It is, contrastingly, one of the great modern ironies that the so-called "liberal" politics in the United States have been resoundingly on the side of taxation, government control, and regulation.
In respect to the case most pressingly at hand, the churches should be free to pay or not pay for whatever they like, not simply because they are churches but because they, like the rest of us, should be free. It is one thing to pass a law saying that insurance may be provided for contraceptives. (Let us assume for the sake of argument that we are not going to be as restrictive as Catholic guidelines morally, but also that by contraceptives I do not mean the clearly immoral abortifacients.) It is quite another to pass a law demanding that insurance must be provided for the same contraceptives. The former clarifies (or, depending on the previous law, establishes) a liberty; the latter imposes restrictions and demands. It would be one thing to author a law permitting alcohol to be sold by any purveyor of foods, without any special license; it would be something else entirely to demand that all grocery and convenience stores stock alcohol - not least because in our modern legislative climate the bill would probably be three hundred pages detailing what ratios of stock of different liquors must be had and imposing fines for stocking the wrong things. (To go back to the general point at hand, for that matter, it is one thing to allow any insurance to be bought corporately (as opposed to individually, which in fact is how some insurance must now be purchased); it is something different and abusive of liberty to demand that corporations must purchase or provide employee insurance - the employer (who is also a person with his own freedoms) has his liberty restricted by such a law.)
All this is clear if our liberty is the greatest political good, an opinion which was fairly clearly the driving force behind the American founding, most especially in the Declaration and attendant publications from the Revolution. Whether or not that remains tenable I will address in the next installment.