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".
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).
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".