It is important to be clear about the fact that the recent Supreme Court decision in Burwell v. Hobby Lobby Stores , the case involving the Health and Human Services contraception mandate, was not decided on constitutional grounds, rather it was based entirely on the court’s reading of a congressionally enacted statute. As Justice Ginsberg noted in her dissent, any First Amendment Free Exercise Clause claim that might have been asserted would have been foreclosed by the Supreme Court’s 1990 decision in Employment Division, Dept. of Human Resources of Oregon v. Smith. 
In the Smith case two men, Alfred Smith and Galen Black, were fired from their jobs with a private drug rehabilitation organization because they took peyote for sacramental purposes at a ceremony of the Native American Church, of which both were members. They applied to Oregon’s Employment Division for unemployment compensation, but were determined to be ineligible for benefits because they had been fired for work-related “misconduct.” Thus, the Supreme Court was called upon to decide whether the Free Exercise Clause of the First Amendment permitted the State of Oregon to include religiously inspired peyote use within the reach of its general criminal prohibition on use of that drug, and, therefore, permitted the State to deny unemployment benefits to persons dismissed from their jobs because of such religiously inspired use.
In a majority opinion authored by Justice Scalia, the court held that the Free Exercise clause did not exempt Mr. Smith and Mr. Black from the operation of generally applicable laws that were not directed at their religion. Since the impact of the law against the use of peyote was “a generally applicable and otherwise valid provision,” the court reasoned, the impact on the religious practice of the Native American Church was only incidental, and did not offend the First Amendment. The “right of free exercise,” the court said, “does not relieve an individual of the obligation to comply with a ‘valid and neutral law of general applicability on the ground that the law proscribes (or prescribes) conduct that his religion prescribes (or proscribes).’”
Justices Blackmun, Brennan, and Marshall dissented in Smith. It is worthy of note, here, that Justices Brennan and Marshall were regarded as “liberal” justices, and Justice Blackmun wrote the majority opinion in Roe v. Wade. Justice Scalia was, and remains, considered to be a “conservative” justice. It is interesting how the “liberal” and “conservative” sides of the court seem to have switched positions regarding the legality of governmental imposition on religious belief and practice. Cynics will draw what conclusions they may.
The sea-change that was being brought about by the Smith decision was not lost on Justice Blackmun. As he said in his dissent:
“This Court over the years painstakingly has developed a consistent and exacting standard to test the constitutionality of a state statute that burdens the free exercise of religion. Such a statute may stand only if the law in general, and the State's refusal to allow a religious exemption in particular, are justified by a compelling interest that cannot be served by less restrictive means.
“Until today, I thought this was a settled and inviolate principle of this Court's First Amendment jurisprudence. The majority, however, perfunctorily dismisses it as a ‘constitutional anomaly.’”
There was outrage at the Smith decision from both the left and the right of the political spectrum. The American Civil Liberties Union (ACLU) had this to say about the case:
“Religious freedom is a fundamental human right that is guaranteed by the First Amendment’s Free Exercise and Establishment clauses. It encompasses not only the right to believe (or not to believe), but also the right to express and to manifest religious beliefs. These rights are fundamental and should not be subject to political process and majority votes. Thus the ACLU, along with almost every religious and civil rights group in America that has taken a position on the subject, rejects the Supreme Court’s notorious decision of Employment Division v. Smith.” 
In response to Smith, the Coalition for the Free Exercise of Religion was formed in 1991.  It was a diverse group that represented at least 70 religious groups and civil rights organizations, including the ACLU, the National Association of Evangelicals, the Latter-Day Saints, the United Methodist Church, and the Traditional Values Coalition. The purpose of the coalition was passage of the Religious Freedom Restoration Act (RFRA), which was indeed passed in 1993 by Congress, unanimously in the House of Representatives and with only three dissenting votes in the Senate , and signed by President Clinton.
The RFRA restores the stricter scrutiny of the Supreme Court cases before Smith. Specifically, the act provides that “Government shall not substantially burden a person’s exercise of religion even if the burden results from a rule of general applicability,”  with this exception:
“Government may substantially burden a person’s exercise of religion only if it demonstrates that application of the burden to the person—
“(1) is in furtherance of a compelling governmental interest; and
“(2) is the least restrictive means of furthering that compelling governmental interest.”
It was intended that the RFRA would apply to both the state and federal governments. But the Supreme Court held in Boerne v. Flores, a 1997 case, that the Congress had overreached its power in trying to apply the RFRA to the states.  Since Hobby Lobby, however, involved a challenge to a federal regulation, the RFRA was applicable. That made all the difference. There was no way Hobby Lobby could have prevailed under Smith. The HHS contraception mandate is a law of general applicability, and cannot be said to be directed at any religious belief or practice.
But the challenge to the mandate under the RFRA was a wholly different matter. Indeed, it would have been a surprise if the court ruled any differently than it did.
It would have been interesting to see how the court wrestled with the issue of whether the government had a compelling interest in achieving the goals of the HHS contraception mandate. But the court simply assumed that a compelling interest was present. Still the government was required to show that it used the least restrictive method to further that interest. That, the court held, the government failed to do. As the court pointed out, it was difficult for the government to argue that it does not have methods at its disposal that would involve less burden on religion, since it already has in place exemptions for religious non-profits, while still providing their employees with access to cost free birth control through payments made by insurers or third party administrators. Moreover, the court said that the government itself could assume the cost of contraception coverage where the employers have religious objections.
The issue was framed by the court narrowly: whether the RFRA “permits the United States Department of Health and Human Services (HHS) to demand that three closely held corporations provide health-insurance coverage for methods of contraception that violate the sincerely held religious beliefs of the companies’ owners.” These were closely held companies. There is no reason to expect that publicly traded corporations would be able to avail themselves of a religious objection. What’s more, this case was decided entirely under the RFRA. If Congress repealed the RFRA, the Hobby Lobby case would be of no effect. As mentioned, no decision was reached on whether the HHS contraception mandate violates the constitutional guarantee of freedom of religion.
Perhaps, in time, the Court will revisit the Smith decision and overrule it. It would be better yet if the First Amendment was applied according to its terms, and that any law effectively prohibiting the free exercise of religion would be struck down. In the meantime, religious believers should take note of the open hostility to religion that has emerged in certain quarters of the political left. There is no reason to believe that they will stop here.