The conclusion doesn’t seem to follow. All people have race, and so can be externally racist, but you would not consider a white person aggressively critiquing white culture to be anti-white, would you?

Why not?

Yes, you would. Whether speech is racist or not is a characteristic of the speech, not determined by the speaker’s skin colour.

Right, was Luther anti-Christian? Such people are generally called “X reformers”, not “anti-X” as an outsider would be.