Posner notes that “The plenary power doctrine is universally loathed by scholars and some have argued that it is effectively a dead letter.” It may well be that, if faced with the issue, the Supreme Court would change the case law on this. But at this point, the precedents counsel in favor of the constitutionality of such a rule.
2. Posner points out that “blocking American Muslims overseas from entering the country would certainly be unconstitutional.” That is absolutely right: U.S. citizens have a constitutional right to come back to the United States — the government can’t exile citizens even for crimes, much less for having the wrong religion.
3. Posner also notes that “blocking immigration by Muslims would raise complicated international-law questions.” I don’t know enough about the subject to opine on that, but this is also something to keep in mind.
4. As a policy matter, I think that banning entry by Muslims would be a very bad idea, for many reasons. But, like many very bad ideas, it might not be unconstitutional.
UPDATE: See also the post on the subject by Jacob Gershman (Wall Street Journal Law Blog), Steven Nelson (U.S. News), and Eyder Peralta (NPR). Akhil Amar and Stephen Legomsky agree with Eric Posner and me; Laurence Tribe and Daniel Halberstam think the proposal would be clearly unconstitutional (even as to aliens); Michael Dorf, Gerald Neuman, and Stephen Yale-Loehr think it’s a close case (which is consistent with Eric Posner’s and my view, given the possibility that today’s Court would indeed overrule or limit the plenary power doctrine precedents).