You're missing my point. I agree that currently things are much better. But you can't have policies that economically disadvantaged one race over the other and expect that to change over night just because the civil rights movement happened. 

If your parents weren't as well off, you won't be as well off. This manifests itself the most when it comes to education opportunities. The best way to move someone out of poverty is through education, when education is funded by property taxes you can hopefully see where things like segregation are still an issue, even if it's not state-mandated segregation. 

Look at what happens in inner cities between rich and poor neighborhoods and then try to understand why they are rich and poor to begin with (hint: literal racism).

This isn't "your fault" for being white. You just have to be aware of it and hopefully push for policies that make public services more fair for everyone.