He can close the campus, or individual buildings, as any governor can do if use of the properties constitutes a threat to public health and safety, and he can task the state police or Guard to do it. Even if it’s a federal property, if it’s inside a state it is within the state’s jurisdiction, and each Governor is still responsible for the safety of everyone on the property. Mayors too, and sheriffs in unincorporated areas, as I understand it: any mayor could close any church or other building where activities are taking place that endanger public health and safety. Without such powers, Job #1 of city, and state executives to maintain the peace, subsets of which are the protection of public health and safety, becomes a dead letter, a toothless power. As the article states, political considerations may forestall action, and they can later be sued for overreach, but they can’t be prevented a priori from issuing orders they deem necessary to uphold their responsibilities.
Challenges have been made already on free exercise of religion grounds, but nothing in the free exercise clause grants any right to endanger public safety. If a church were holding gatherings where minors were abused as part of some purportedly religious rite, no one would argue the mayor or governor couldn’t, nor shouldn’t, intervene to stop it, including revoking the building’s certificate of occupancy or whatever other means were required to prevent the abuses.
Other challenges have been made on the 1st A’s assembly clause, but like the “well-regulated militia” clause of the 2nd A, they conveniently ignore the qualifying language, which is that there shall be no law restricting the right to “peaceably assemble”. Since an assembly would pose a health threat to the attendees and the community at large, the gathering would be a breach of the peace, and since that is the basis itself for executives’ police powers, it could be forbidden.
To my eye, these powers are well-established and precedented, the fact that anyone’s at all alarmed at their potential use today only shows that they haven’t been used in recent memory, but the powers inhere to the offices nonetheless. Without them, there’s little point in having an executive in any state or city.