I admit it. I haven't actually read the Supreme Court's Hobby Lobby decision, only reports on it. But it is an area that I have at least a strong law school familiarity with, so I might was well weigh in.
First and foremost, this was NOT a First Amendment decision. It was made under a federal statute, the Religious Freedom Restoration Act (RFRA, pronounced Rifra). Making this decision based on RFRA instead of the First Amendment theoretically means that Congress can overrule it by amending RFRA. (Of course, as a practical matter, such a change stands no chance of passing the Republican House). The official reason for that decision is that the Supreme Court will not make a constitutional decision if it can base its decision on statute instead. The unofficial reason is that to decide the case First Amendment grounds could be embarrassing to all involved. The current Supreme Court standard for deciding religious freedom was articulated by Antonin Scalia and says that a neutral statute of general applicability that only incidentally impinges on religious practice is constitutional. In other words, so long as the purpose is not to restrict religious practice, an incidental infringement is allowed. Scalia does not believe that government is constitutionally bound to accommodate religion and instead believes that the appropriate degree of accommodation should be worked out through the political process. At the time he made this rule, many liberal justices protested, saying that government should be made to accommodate people's religions.
It was in response to this ruling that Congress passed RFRA. RFRA forbids government from imposing a "substantial burden" on anyone's religious practice unless it is the "least restrictive means" to meet a "compelling governmental interest." The terms "substantial burden" and "compelling governmental interest" are not defined, either by the statute or the Supreme Court, which means knowing how courts will rule in any given case requires a large measure of guesswork. One term that is defined is "government." Originally, RFRA applied to both the state and federal governments, but the Supreme Court held that, while the federal government was free to impose such a burden on itself, it could not impose such a burden on the states. By the time the Supreme Court made that ruling, it had become apparent that for government to infringe on the religious practice of a free person was actually quite rare. Most RFRA cases involved inmates seeking accommodation of some religious practice that the prison considered a security risk. And whatever else may or may not be a "compelling governmental interest," prison security definitely rates.* So Congress passed the Religious Land Use and Incarcerated Persons Act (RLUIPA, and no, I don't know how that is pronounced) that applied the same standard to any prison accepting federal funds (which is all prisons) and to certain land uses.
As a number of people have commented, up until now RFRA had been presumed to apply to individuals, churches, and Indian tribes (which have tribal religion), but not to for-profit corporations. So extending RFRA to closely held corporations is something new and (to many people) disturbing.
Next comes the question of sincerity of religious belief. Although the courts may not decide under RFRA whether religious beliefs are true or false, they may decide whether they are sincere or insincere. Plenty of people I have read assume that the court must simply assume that all asserted religious beliefs are sincere, but that is an exaggeration. It is not unheard of to find a professed religious belief insincere. Consider the Jehovah's Witnesses, who have religious objections to blood transfusions. Besides refusing to accept transfusions, they also refuse to donate blood, which seems logically consistent. One of the cases I read involved a Jehovah's Witness charged with rape. The state wanted to take a blood sample for DNA testing, but he refused, citing religious objection to blood donation. Numerous church elders submitted affidavits that this was nonsense, and that the Jehovah's witnesses objected only to transferring blood from one person to another, not to taking blood samples for medical or forensic analysis. Given the self-serving nature of his objections and their repudiation by church authorities, the court found that his objections were not sincere. And the courts have found that individual, idiosyncratic beliefs are not sufficient to count as "religious." There must be an institutional religion holding such beliefs. So it would appear that a self-serving belief rejected by church authorities would be considered "insincere." Plenty of opponents have doubts that Hobby Lobby executives' belief that certain contraceptives are really abortifacts are truly sincere. But in the absence of formal repudiation by church authorities, the courts have little choice but to accept their sincerity.**
More troubling is the blurring of the line between a religious and a scientific belief. Religious beliefs are beyond the authority of courts to decide at least in part because they are not subject to proof or disproof. If Evangelical Christians believe that personhood and the rights of personhood begin with fertilization, and that interfering with the implantation of a fertilized egg is morally indistinguishable from infanticide, that has to be treated as a religious belief not subject to proof or disproof and therefore beyond the realm of the courts. But the belief that a certain contraceptive method interferes with implantation is not a religious belief. It is a scientific or empirical belief that is subject to proof or disproof. The blurring of the distinction may open some dangerous doors later on.
Finally, once the Supreme Court rules that closely held for-profit corporations have religious rights, deciding under RFRA instead of the First Amendment merely postpones the day of reckoning. Many employers are raising religious objections to anti-discrimination legislation based on sexual orientation. Others object to making cakes, taking photographs, and the like at same sex weddings. Recall that RFRA applies only to the federal government and not to states. There is no federal anti-discrimination legislation on the basis of sexual orientation. All such cases are under state law. Many of the states with such legislation have their own state RFRA's and all have state guarantees of freedom of religion. But federal courts may not interpret state constitutions or statutes. In many such states, state Supreme Courts have refused to carve out religious exemptions to anti-discrimination laws, either under state RFRA's or state constitutions. Thus photographers, caterers, and others ordered to participate in same sex weddings are without recourse under state law. Federal RFRA cannot help them, because it applies to the federal government only. That leaves the First Amendment as their only recourse. Make no mistake. Now that the Supreme Court has ruled that closely held corporations have religious rights, sooner or later some of them will start seeking vindication under the First Amendment where it is not available under state law or RFRA, and then the Supreme Court will have to decide. It will be interesting to see what they do.
*And rightly so. One can question whether any governmental interest other than public safety is "compelling" enough to override a constitutional right, but public safety is the supreme compelling governmental interest, and prisoners are part of the public.
**Come to think of it, this might be a good use for Sarah Palin's word "refudiate," which appears to be a cross between refute and repudiate. Church authorities in the Jehovah's Witness case were really doing both. Refudiation!