Oh, absolutely. Keep in mind that this novel was set in the time period of the 1930s, but it was written by Harper Lee in 1960. What she wrote about racism still existed in 1960, and it still exists today. Not that achievements haven't been made - but achievements will not erase the prejudicial tendencies of a society, even if they do help prevent against discrimination. Lee writes about the attitudes of the whites towards the blacks, and the other way around. They have trouble trusting each other, the feel different than each other. The kids feel just as odd going to Calpurnia's church as Tom Robinson felt going into the Ewell house. Today, those feelings of fear and distrust still exists, whether it be from whites to blacks or Americans to immigrants.. etc. Look at the riots that took place in Los Angeles 10/15 years ago, when members of the black community began physically attacking white citizens without caring who the person was. Look at the reactions towards Arab Americans after 9/11 - racism still does exist.
On a happier note, however, the courage shown by so many characters also still exists. The hope that humans have for a better future, and the way that communities will band together to help each other out - all of that still exists, too. Times change and people change... but slowly, and never very much.