Further, I'm very interested to know what is so special about stereotyping that makes it not susceptible to this kind of argument.
Because as you said, killing can be justified or morally unjustified depending on the circumstances. I don't see an instance where stereotyping is legitimate, assuming that it is bad in general.
This seems like such a strange argument for someone as obviously clever as you to make. So
killing is not "bad in general" but
stereotyping is? For one, stereotyping -- making an oversimplified opinion or judgment, usually based on an overly limited set of characteristics -- seems like a much more neutral activity than killing. Yes, it's
always bad in the sense that a stereotype is, by definition, reductive, but by that analysis, all logical fallacies are always bad -- unjustifiable or wrong, in your terms. Further, isn't there a harm analysis here? I'm the first one to argue that certain racial stereotypes have important real-world consequences (for instance, I'm currently reading an article titled "Looking Deathworthy: Perceived Stereotypicality of Black Defendants Predicts Capital-Sentencing Outcomes"), but killing is killing. Dead is dead. Come on!
Stereotyping is much more analogous to another fallacy, like an ad hominem attack, in that it is not the best form of discourse, and it may be truly damaging or assaultive, but it could also be funny or true or justified, depending on the circumstances.