I’m not sure how seriously they’re taking the appeal, but it’s still cause for concern. In light of Oregon v. Smith, the argument that the contraceptive mandate violates the First Amendment should be laughed out of court, but in a context in which ad hoc arguments that the PPACA violated the commerce clause could get 5 votes from the Supreme Court all bets are off. And the fact that Scalia wrote Smith guarantees nothing — as NFIB v. Sebelius showed, he’s not going to consider himself bound by his previous holdings in landmark cases or anything.
…a commenter argues that the real argument will be based on the Religious Freedom Restoration Act. I don’t think this actually works, because although RFRA might apply the old Sherbert standard to lower federal officials, it’s not obvious to me that it should be seen as applying to future legislative enactments — it seems to me that the proper course is to assume that the more recent legislation supersedes the older one. But even if we assume that the Sherbert test should apply, the argument is still utterly frivolous. If the RFRA prevents the application of federal law in this case — which concerns a de minimis burden on religious practice, and indeed would result in a substantial net reduction of religious freedom — I’m not sure what significant federal law you can enforce.