Where does the Bible teach against racism and slavery?

True Christianity preaches the opposite of racism, slavery, and hatred. True Christians acknowledge that all mankind was made from one blood (Acts 17:26), and therefore dividing humanity according to physical features (i.e., race) is not a biblical concept. In fact, the concept of race itself is a manmade distinction intended to provide support for human prejudice. 

In truth, the color of human skin, as well as other physical features like the color of human hair, eyes, and other features all, vary along a spectrum that God designed. God never assigns any meaning to these differences, and therefore we should enjoy the diversity of human appearance in the same way we enjoy the variety of flowers or foods or sounds in nature. Only human sin is responsible for turning mankind's natural physical differences into a justification for prejudice, mistreatment and even slavery. Neither Christianity nor the Bible advocates or even support such sin. 

Therefore, those who would suggest that Christianity must be rejected on the basis of race concerns or historical prejudice are disingenuous or deceived. We suspect many are likely unbelievers looking for a cause to insult Christ and reject the Gospel, especially those who also promote pagan religions or the occult as an option to faith in Christ. 
Therefore, you counter such teaching simply by preaching the Gospel, since those who say such things are most likely ignorant of the true Gospel of Jesus Christ.

As Paul said himself about reaching pagans with the truth:

1Cor. 1:18  For the word of the cross is foolishness to those who are perishing, but to us who are being saved it is the power of God. 
1Cor. 1:19      For it is written, 
    “I will destroy the wisdom of the wise, 
    And the cleverness of the clever I will set aside.” 
1Cor. 1:20 Where is the wise man? Where is the scribe? Where is the debater of this age? Has not God made foolish the wisdom of the world? 
1Cor. 1:21 For since in the wisdom of God the world through its wisdom did not come to know God, God was well-pleased through the foolishness of the message preached to save those who believe. 
1Cor. 1:22 For indeed Jews ask for signs and Greeks search for wisdom; 
1Cor. 1:23 but we preach Christ crucified, to Jews a stumbling block and to Gentiles foolishness, 
1Cor. 1:24 but to those who are the called, both Jews and Greeks, Christ the power of God and the wisdom of God. 
1Cor. 1:25 Because the foolishness of God is wiser than men, and the weakness of God is stronger than men. 
1Cor. 2:1  And when I came to you, brethren, I did not come with superiority of speech or of wisdom, proclaiming to you the testimony of God. 
1Cor. 2:2 For I determined to know nothing among you except Jesus Christ, and Him crucified. 
1Cor. 2:3 I was with you in weakness and in fear and in much trembling, 
1Cor. 2:4 and my message and my preaching were not in persuasive words of wisdom, but in demonstration of the Spirit and of power, 
1Cor. 2:5 so that your faith would not rest on the wisdom of men, but on the power of God.