I submit that the court decision discussed here by Ron Lindsay is wrong in principle. The outcome is to allow a religious publisher to evade the contraceptive mandate, and not offer its employees insurance cover with provision for contraceptives. Thus, the effect is to restrict the effect of a religiously neutral law of general applicability to employers (religous or otherwise) in the US. Such a law does not impinge on freedom of religion, as understood within the neo-Lockean model that I argue for - and which is pretty much accepted by the US Supreme Court in interpreting the First Amendment.
Importantly, persecution or imposition of religion in no way motivates the contraceptive mandate provision. Nor can it be said to be the primary effect of the law, or even some kind of disproportionate effect such as to make the law appear to be a contrivance or something of the sort. Nothing like any of this is involved. In principle, the law should have been upheld and left to operate freely.
If the case had been decided, with the same outcome in favour of the religious employer, under the First Amendment, I'd be fairly confident that it would be overturned on appeal. Note, however, that it appears (from Ron Lindsay's discussion) to have been decided under the Religious Freedom Restoration Act, which goes a lot further to give parties before the courts an affirmative right to practice their religions, which can include complying with religious canons of conduct, even in the face of neutral and general laws enacted to provide citizens with worldly benefits.
The Religious Freedom Restoration Act was a mistake. It gives rights to religion that go well beyond the historical point of religious freedom, i.e. to prevent the state from imposing a favoured religion or persecuting a disfavoured one. The statute did not restore religious freedom. Rather, it created a situation where religious individuals, organisations, etc., obtained legal rights in excess of religious freedom.
The effect of the Act was struck down at state level by a US Supreme Court judgment, back in the 1990s, but it continues to apply at federal level in the US (and in addition, some states have their own versions of it). The effect is to impede the federal legislature in defending perfectly legitimate, non-persecutorial laws when they are challenged in the courts. Instead of the situation being clear-cut under the Supreme Court's interpretation of the First Amendment, litigation over cases of "religious freedom" is now a dog's breakfast, as is trying to draft laws to conform to its requirements. This is an unsatisfactory situation, but I doubt that anything can be done about it in the short or medium term.
It's at least worthwhile, however, pointing out the problem. More people should be doing so. The Religious Freedom Restoration Act did not "restore" religious freedom in the US - something that the First Amendment protects adequately and did not need to be restored. It goes further and gives religious people and institutions - and even for-profit corporations - a special privilege to challenge neutral and general laws that they find inconvenient.