My question came after reading that as well: I have to wonder whether this was a sort of Galois-style statement open to an interpretation of incitement of violence, or whether it simply a statement of Trump's actions being horrible for research. Neither case would be good, but the former would be more understandable than the latter.

What do you mean «Neither case would be good»? Not clear.

Example: Gary Marcus wrote six weeks ago, «single-minded obsession with cutting costs is going to cripple science and American universities, with horrific lasting consequences» - that falls into your «...actions being horrible for research», but how does it fit with your statement of a "good case".

I imagine something like neither case (of getting arrested for such) would be good

Speaking of statements open to misinterpretation... sorry, as the other commenter imagined, I meant that refusing entry for either type of statement would not be good, but one would be worse than the other.

Refusing a foreigner entry for inciting violence (even against people who are not Americans and not in the U.S.) would be perfectly fine with me, though I don't approve of demanding foreigners make all their communications available to CBP (which is basically how we got here).

I do wish we’d have better sources since there could be a range of jokes about the two shooters during the campaign which could get close to a plausible threat, but the fact that they just shipped him home makes that seem less likely. If you thought he was Carlos the Jackal you’d probably at least hold him long enough to investigate his travel plans and contacts more.

Yes, I think the actual contents of those messages would make all the difference in assessing the US response.

Note, too that last month two researchers (yes, actual researchers) threw bombs at a Russian consulate in France, so the argument that messages are just banter among friends and that academics would never actually do anything 'stupid' has been severely weakened.

The problem is surely that by considering opinions against the U.S. administration, that it produces a large number of non-compliant visitors. I think it's counter-productive as it just means that most visitors would then have a good reason to hide accounts and conversations. I suppose it "works" in reducing the number of visitors, but is that really of any benefit to the U.S.?

I think it would provide better intelligence if the more casual criticisms of policy were ignored and more attention paid to violent/threatening content. This would allow authorities to focus attention on other people involved in the communication which would probably be of more benefit than trying to target all visitors that disagree with policies.

The rules absolutely change along with the President. The President has total discretion about which non-citizens are allowed entry. Just a few days after Trump took office the first time around, he unilaterally banned people from a bunch of countries from entering. If Trump told CBP to deny entry to anyone found making critical statements of him, that's probably legal and even if it wasn't the illegality probably couldn't be enforced. More likely, this is preemptive compliance, where either the agent feels emboldened to make this determination on his own, or thinks it's what the boss wants. Individual agents have free reign to deny non-citizens entry.