It depends on the situation.
If, for example, we are in the same thread and you guys are talking about how the N word isn't offensive because you aren't Black and so therefore people who are offended need to suck it up because most people on the planet aren't Black and as such, won't be offended by it, and then the thread turns into an ongoing list of racist jokes against Blacks, then I would say I, or anyone else who is offended have the right to say something about it. Just as you or anyone else would if the roles are reversed.
Being in the majority doesn't give you the right to dictate a person's feelings, or to write them off completely, and for the sake of discussion, you should at least try to be empathetic or understanding of the other person's point of view, instead of writing it off completely as that person over-reacting. Especially since, you would likely want the same chance if you were in that situation.