Let's boil this problem down. Is it fair to say that, either this problem is innate or, it is experienced and learnt. Its either one or the other. I would defer from considering children here for a while because it is suffice to say children know no racism. I don't know of a single case. Adults exhibit racism. No need for beispiel. Then why are some adults racist, some are not. For adults, I want to know when they exhibit racism, is it an instinctive tendency (thus biological) or was it the lump sum of exposure/teaching, direct/indirect, throughout childhood and adulthood?
But before moving on, one might say, Aha!, if it were to be innate/instinctive, why wouldn't a child be racist? For that, I stick to the fact that a child has limited experience and knows no effort for survival or sustenance.
Now it can be pointed out that, "you would try to protect/befriend/serve the different-raced stranger who wants to give you a meal a day more than you would protect/befriend/serve the same-raced stranger who wants to take from you your meal". A child has no selfish interest (for survival or sustenance), an adult does.
But let me point this out. Selfish interest is what one would do to guard his/her selfish interests, that ensures his/her survival, that would ensure that his/her genes gets passed on. So as a theory, one would always act in a way to guard ones own selfish interests innately/biologically. So it is rather circumstantial what ones selfish interests are at the time. It is always there though, in our genes, to act to guard ones selfish interests. So, I'm not saying that evolution has made us racist, but rather, racism stems out of our innate tendency to guard our selfish interests under given circumstances.
And out of that tendency, it once came and stayed. Humans use culture and memes to guarantee their reproductive success, using racism to cut out competition. If a large-scale meme was created that countered the genealogical tendency to exclude outsiders, and it was successful, racism would no longer be a strong mechanism to guarantee gene replication. Instead, the tendency for it would lessen because it is no longer desirable or convincing.
Then, to sum up, racism is a meme that can survive due to in group out group tendencies. We have a predisposition to notice all differences in each other and to protect people we are common with. The racist meme takes advantage of that and encourages people to see the color difference as significant and to believe that that difference is highly dangerous. Even though, if left to our own nature, we conclude it's not and notice instead if they like the same baseball team, etc.