That is a talking point I have been hearing increasingly on talking-heads shows. It is not quite true. From a handy blog post from the U.S. Conference of Catholic Bishops:

6. The federal mandate is much stricter than existing state mandates. HHS chose the narrowest state-level religious exemption as the model for its own. That exemption was drafted by the ACLU and exists in only 3 states (New York, California, Oregon). Even without a religious exemption, religious employers can already avoid the contraceptive mandates in 28 states by self-insuring their prescription drug coverage, dropping that coverage altogether, or opting for regulation under a federal law (ERISA) that pre-empts state law. The HHS mandate closes off all these avenues of relief.