To get rid of racism, many factors play a role in my opinion. Most important is to avoid votes for racist or nationalist people / parties. Second to ensure equality by law. In the US, there are still many people preventing this. Well known was for example stop and frisk.
Bitcoin can't help there but it can help to show what's important in a society. Bitcoin has a very international community like here on Bitcointalk (well if we avoid some racists in P&S ) and it doesn't matter where you are from to use it (except if you don't have infrastructure). It can bring people together instead of dividing them. People will start to know that a racist, divided society has less power than a non-racist, united society (like Bitcoin).

The role of Bitcoin isn't a big one here but it can be one part of many factors.