As usual, Yuval is correct when he writes that the proposed revised birth control rule constitutes greater, not lesser, intrusion into the religious realm by the Obama Administration. I get into it as well over at Human Exceptionalism. In a nutshell, here is how the slight of hand works.
[Correction: Upon closer look, a reference to a tax code section in the proposed rule means the old exemption for "churches" remains. All other religious organizations only receive the accommodation described by Yuval. There is no opt/out for having their female employees covered for contraception for these groups, as referenced in 3 below. Sorry for any confusion.
1. Treat all religious non profits—whether houses of worship or organizations like universities—alike. That would have been good if the current exemption for houses of worship had been expanded to all dissenting religious organizations. But that isn't what the government is proposing.
2. Do away with the existing full exemption for houses of worship, reducing it to a mere accommodation for all religious non profits opposing contraception.]
3. Require all employees of opposing religious organizations to receive birth control coverage through a separate policy, paid for by the insurer.
Thus, as I note at HE: If a religious organization has 50 employees, it must provide health insurance. The mere act of providing health insurance requires insurance companies to pay for contraception, sterilization, and abortifacients. In other words, nuns (and all female religious employees) will be covered for birth control whether they want it or not.