Racism is a sin, and because we live in a sinful world, racism will always be a potential danger.
But that must never be an excuse for racism, or for failing to do what we can to overcome it. Murder is a sin–but God doesn't want us to shrug our shoulders and not stop people from killing each other. In the same way, racism is a sin, and God doesn't want us to ignore it or refuse to do whatever we can to combat it.
What is the real problem behind racism? What makes people of one race (or tribe or language) hate those who are different from them? The real problem is within us–within our own hearts and minds–and only when our hearts are changed will we learn to love and accept others as we should. Jesus said, "For out of the heart come evil thoughts, murder, adultery, sexual immorality, theft, false testimony, slander" (Matthew 15:19).
That is why our greatest need is to turn to Christ and allow Him to come into our lives and change us from within. He can take away our pride and our hatred of others, and replace them with His humility and love.
I am grateful for the progress that has been made during my lifetime in race relations–but (as you say) much more needs to be done. May God help each one of us to search our hearts and yield ourselves to Christ, and then reach out to others with His love.