Of course babies can discriminate, in the meaning of "tell the difference between" - but they don't CARE about the difference until some grown-up makes them.
My kids used to refer to people by the color of their clothes, as in, look at that black guy over there (to someone of any race at all, wearing a black shirt), but they would be pointing out something interesting, like He's dancing in the rain, not just the fact that he was "black" (in any sense).
My kids are white and have suffered from racial discrimination, in their majority-black middle school. (No, you can't play with us, honky!) But they understand that if people who are black are fighting, it's the fighting that's the problem, not the fact that the fighters are black, since that wasn't exceptional.