No, the Bible does not support racial prejudice of any type. God created the whole human race and His love extends to the whole human race–and so should ours. The Bible says, "From one man he made every nation of men, that they should inhabit the whole earth" (Acts 17:26).
Furthermore, the Bible teaches that Jesus Christ died on the cross for people of every race, and when we know Christ, we are one in Him. The Bible says, "There is neither Jew nor Greek, slave nor free, male nor female, for you are all one in Christ Jesus" (Galatians 3:28). And some day in heaven we will be together, for by His blood Christ "purchased men for God from every tribe and language and people and nation" (Revelation 5:9).
Perhaps your parents' views came from the way they were raised, or from some experience in the past–but let me assure you that they did not come from the Bible. Pray for them and gently let them know you value all of your friends, regardless of their race.
Most of all, don't let their views keep you from Christ. God loves you (and them), and Jesus died to save people of every race–including you. Have you responded to His love by opening your heart to Christ?