You're not solving the problem at all by attempting to sweep racism under the rug; quite the opposite in fact because it fails to address how race affects family background and discrimination in the first place.
You seem to have misunderstood my argument; maybe I wasn’t really clear in that part. I think a policy that helps lots of poor black people, some poor white people, and doesn’t help Obama’s daughters (because they don’t need help), is a good, fair, and most importantly effective policy. A policy that doesn’t help poor white people is racist. A policy that helps Obama’s daughters is ineffective (and I don’t want my tax money to go to that cause).
We have affirmative action policies and the like because we admit that some groups of people are disadvantaged due to a multitude of circumstances and we attempt to do things in such a way as to ensure that they can mitigate those circumstances.
Providing aid to low-income families is racist by the first definition, but not by the second. But (damn near) everything is racist by the first definition.
It would seem you are the racist here thinking a person needs support because he is black, not because he is poor.
In your example help isn't given to all black people, only to the poor ones.
If you consider help given to poor black people vs. help given to poor white people, it becomes proportional.