I am assuming we are talking about "skin-colour" groups here, meaning the only thing I have in common with everybody else in "my" group is that the colour of our skin happens to be the same or at least of a similar shade.
Stereotyping based on groups like that is bigoted and racist, so.. That's why I said that the onus should be on the person making the stereotypical/bigoted/racist statement, and not the person being grouped in with other people based solely on the colour of their skin.
Isn't this what is called "victim shaming" ? The onus is on the person saying the stereotypical/bigoted thing, i.e. they should stop making statements like that, and not on the victim who is the target of the statement.