(This generalizes, so women can be sexist against other women; those in poverty can be classist against other poor people. To take a recent interview: "Women are always the first to discredit other women, likely because they’ve personally experienced something worse and didn’t or couldn’t speak up for themselves." https://modelviewculture.com/pieces/interview-with-julie-ann... )
When discussing racism, it's not just about racist emotions. Also about institutional outcomes, which can be impersonal.