"Denying women the vote isn't sexist, because some women said so!" (True story.)
Or pointing to people like Malcom X who wanted Blacks to separate as evidence for segregation because "Blacks don't really want to integrate."
I doubt the cop thing is self prejudice as much as needing to fight the prejudice in the line, so they work double hard to "fit in". "Yes, of ocurse i can do my job and arrest black people even if i'm black" etc.
And the use of "she is an X, and if she said it, it must be true" is part of the world of privlidge. using other people to make your point.