I always say "That's cool" first. Why is it so difficult for some, many, most White people to say, "That's cool" first? It comes from a deep lack of empathetic preparation. They have a certain area, amount, and-or appropriation set aside for themselves (us Whiteys) and it is like pulling short hairs to give it up.
Unfortunately, I am not totally free of this set aside. My gender and skin color biases are tamped down more than most, but it shows up internally and (almost?) never externally. That said, I think one of the best ways to remove it is to admit to these prejudices. Any Whitey that says I am not a racist, or male that says I am not a sexist/genderist, etc., gets in the way of removing these damaging prejudices.
"Externally" my wife and I have never taught our daughters to hate or look down upon, etc. Keeping our internal biases away from them, purposefully (by our personal doings/sayings) or "naturally" (because we were taught to be less prejudical by our parents as well) they will be less biased. Over a couple generations we "could" wipe prejudice out.
Whiteys (and men) who take themselves (and their skin color and-or gender) too "seriously" ensure that their children will continue with prejudicial/biased perspectives, traits, and actions.
We all have reptile brain functions. Feeding the reptile tons of empty calories forever means it just shits out more lumps of dumbass. Feed it good calories (bias free info) and it will shit out less (racism/sexism/etc) and the human frontal lobe will have a chance to get on with the better side of humanity. This one idea alone will not make things change overnight or magically, but it is a good place to start.