Most people consciously or unconsciously buy in to the dominant racist paradigm at least some of the time. If you take little kids and show them a black doll and a white doll, regardless of the race of the child, when asked "which doll is smart?" or "which doll is a nice person?" kids of all races pick the white doll. Believing in these kinds of biases supports racism even if one "has black friends" and never says the N-word and agrees with MLK in the abstract.
And at the same time most people buy in to these ideas most people of all races think "racism is bad." Hence talking about racism is at time difficult. People who I love and are dear to my heart have done racist things from time to time. But they remain friends (and family) because, when I talk to them, they don't just shut down at to topic of racism... rather they listen. And some of the time I realize that I was the one who was wrong. Other times they are like "oh wait. yeah. That IS racist. Shoot!" And they see that I'm right. And some of the time we can't agree, and even that can be OK.
It's not that hard.
Many people think of racism as crude and bad manners-- It's seen as "low class" to be racist. It's seen as "poor form." This racism as manners way of seeing things has helped a little. Few people say the n-word as a racial attack anymore. The trouble is eliminating racism is more than just eliminating "bad manners" or "bad words" it is about creating a culture of common respect where black people and blackness are not regarded as primitive or inferior. Where gay men were seen as "real men" --Where transgendered people are not thought of as "its" --where Asian men are not seen as small and effeminate and black women are not presumed to be masculine and butch-- where a Chinese girl can be good at math without anyone thinking "it's just because they are so good at math" -- where a black person who is good dancing causes people to think "he must practice a lot!" rather than "he has natural rhythm..." When the word "nerd" doesn't automatically mean "white male" --
The funny thing is all of these stereotypes come directly from the racist philosophy of the 19th century-- even the (so-called) "positive" stereotypes. (Like the one that black men are well-endowed) -- they all relate to the notion that African people are closer animals, Asian people are robots and white people are normal, creative and smart.
It's not possible to be anti-racist without interacting and seeking feedback and giving feedback. It's not possible to not be racist if you never talk with black people about racism. It's not possible to stop being homophobic without talking to gay people about homophobia. If you are white, for example, listen and talk to non-white people about racism. Argue a little even! Defend your views, but be willing to change if you are wrong. Don't try to shut down the whole conversation or change the subject. (i.e. things like "that may be racist but why is it that black people can say N8gg## and get away with it!? HMMMM?" ) If you only agree ever that something is racist when it strikes you personally as being racist first-- you're missing some things. Take in what people are saying before you condemn it. If you always, 100% of the time, disagree when a black person says "hmmm that's racist!" -- you're probably being too defensive. If you agree maybe 50% of the time when black people says "I think that is racist" -- maybe you are getting someplace.