Does a stereotype need to be largely false to be objectionable? Many people seem to think so, as when they respond to criticism of stereotypes by replying, "Some stereotypes exist for a reason."

"Largely false" is an interesting phrase -- and there are several different things one might mean by a stereotype, and it's being "true" or "somewhat/largely" true ... plus there are different sorts of "offenses" one may commit when using stereotypes -- but to be brief: Let's assume some stereotype is largely true, i.e. true of many/most of the members of the relevant category. One might still proceed objectionably when using that stereotype simply for assuming that what's true of many/most is in fact true of all. Indeed, we sometimes say that fail to treat an individual with appropriate respect when you simply classify that individual as a member of some category and are disinterested in the particular details that might characterize that individual. So even if the stereotype is true of that individual, it may still be wrong to ASSUME it is true of that individual; and all the more so if it turns out the stereotype is not true of that individual. So a short answer to your excellent question is no: even ...