It's a bit of both, but mostly nurture.
We're naturally going to distinguish "like" from "unlike." A white guy is like a black guy in the sense that they are both male, but unlike in the sense that they're different colors. his may breed either a like or dislike of one or the other, the potential for both is there.
I'm willing to bet that most white people have mostly white friends, most black people have mostly black friends, and so forth and so on. This topic was brought up in one of my sociology classes, and one girl said, "Well, white people tend to live in mostly white neighborhoods, and black people tend to live in mostly black neighborhoods." (I'm paraphrasing, it was a few years ago.)
My professor asked what the class thought, and I said the exact same thing as I said above, and the girl who was trying to pull the racism card didn't have any argument to the fact.
It's not really a "race" issue so much as one of class and culture. Think about it. Would you rather have someone of similar class and culture watch your child while you're away, or would you rather have someone that different from you in both looks and culture, even if yor class is the same or similar?
Children don't even distinguish color until the age of about four or five anyway, so it's unlikely that nature has a huge part in it unless the stuff mentioned above is taken in the wrong direction.
In short, if you're nurtured to focus on the negative sides of the unlike, which is noted by nature, then you'll likely end up racist.