JayMatt,
1. “Kivan sheNitan reshus…” is not universally applicable but is a definite precept from Chazal, despite the many, many, instances where Hashem did, does and will differentiate.
2. We see from Chazal that protesting is sometimes called for. There are other cases, by goyim, too, such as Moshe Rabbeinu when Yisro’s daughters said Ish Mitzri, etc.
I can’t tell you one can directly extrapolate from Korach to this. But the concept is definitely there, and if gedolim say to protest it then this Chazal seems to be at least a “deyka” or indicator that this is, in fact, correct.
3. Lot would have been destroyed in Sedom, too, were it not for Avraham Avinu. The shachain part may refer to Jews (or may refer to non-Jews, too). But it’s not only a Jewish-Jewish relationship.