Acts 10:34-35 Opening his mouth, Peter said: "I most certainly understand now that God is not one to show partiality, but in every nation the man who fears Him and does what is right is welcome to Him."
One of the basic teachings of the Bible, especially the New Testament, is that Christians are called to be "Christ-like." Christ is God, God is Christ, and along with the Holy Spirit you have the Holy Trinity. To be Christ-like is to act as God would act. Furthermore, Old Testament Genesis says that man (humans) are created in the image of God. Whether that is physically looking like God or emotionally/spiritually/intelligently resembling God is not explained. The verse from Acts says that God does not show partiality to people. If God doesn't people shouldn't either. God asks for faith and trust in him. Which race that comes from doesn't matter.
John 7:24 "Do not judge by appearances, but judge with right judgment.”
That verse is a quote. The speaker is Jesus, and he is speaking to a crowd of people. Some people in the crowd are angry with Jesus for a variety of reasons, and Jesus defends himself at one point with the above verse. Jesus is not telling the people to never judge. He is telling them not to judge based on appearances (like skin color), but to judge based on actions and words.
James 2:9 "But if you show partiality, you are committing sin and are convicted by the law as transgressors."
This one is fairly straightforward. If you show partiality, for any reason, you are committing sins against that person and God's law. It could be favoritism and partiality because of race, sex, economic level, group clique, etc. The Bible teaches that is wrong.