In today's Austin v. U.S. Navy Seals 1–26, the Supreme Court stayed "[t]he district court's January 3, 2022 order, insofar as it precludes the Navy from considering respondents' vaccination status in making deployment, assignment, and other operational decisions … pending disposition of the appeal in the United States Court of Appeals for the Fifth Circuit and disposition of the petition for a writ of certiorari, if such writ is timely sought." (The Fifth Circuit had earlier denied the stay.) The Court didn't explain its reasoning, but one member of the majority, Justice Kavanaugh, did:
I concur in the Court's decision to grant the Government's application for a partial stay of the District Court's preliminary injunction for a simple overarching reason: Under Article II of the Constitution, the President of the United States, not any federal judge, is the Commander in Chief of the Armed Forces. In light of that bedrock constitutional principle, "courts traditionally have been reluctant to intrude upon the authority of the Executive in military and national security affairs." As the Court has long emphasized, moreover, the "complex, subtle, and professional decisions as to the composition, training, equipping, and control of a military force are essentially professional military judgments." Therefore, it is "difficult to conceive of an area of governmental activity in which the courts have less competence." …
[E]ven accepting that RFRA applies in this particular military context, RFRA does not justify judicial intrusion into military affairs in this case. That is because the Navy has an extraordinarily compelling interest in maintaining strategic and operational control over the assignment and deployment of all Special Warfare personnel—including control over decisions about military readiness. And no less restrictive means would satisfy that interest in this context.
The Court "should indulge the widest latitude" to sustain the President's "function to command the instruments of national force, at least when turned against the outside world for the security of our society." That fundamental principle applies here. As Admiral William Lescher, Vice Chief of Naval Operations, explained: "Sending ships into combat without maximizing the crew's odds of success, such as would be the case with ship deficiencies in ordnance, radar, working weapons or the means to reliably accomplish the mission, is dereliction of duty. The same applies to ordering unvaccinated personnel into an environment in which they endanger their lives, the lives of others and compromise accomplishment of essential missions."
In sum, I see no basis in this case for employing the judicial power in a manner that military commanders believe would impair the military of the United States as it defends the American people.
(Note that Justice Kavanaugh isn't arguing, as I understand it, that the President has exclusive powers here; article I, after all, gives Congress the power "To make Rules for the Government and Regulation of the land and naval forces," and RFRA, as applied to the military, may well be such a rule. Rather, I take it that he's arguing that courts ought to be especially hesitant preempting the Executive's judgment in applying any such legislation to the military's operations.)
