How did the colors of the human race originate? Was it a Christian classification?
You can read about the classification of the human race into colours on Wikipedia. None of the classifications are specifically Christian. While there is some writing on this subject in early Greek literature, the earliest widely accepted classifications are from Medieval Rabbinical (Jewish) writings. These classifications are based on the sons of Noah. For example:
In Hornius' scheme, the Japhetites (identified as Scythians and Celts) are "white" (albos), the Aethiopians and Chamae are "black" (nigros), and the Indians and Semites are "yellow" (flavos), while the Jews, following Mishnah Sanhedrin, are exempt from the classification being neither black nor white but "light brown" (buxus, the color of boxwood).
Carl Linneus in the 1730s talked about four human subspieces:
Americanus (Americans), Europaeus (Europeans), Asiaticus (Asians) and Afer(Africans).
Blumenbach also wrote of four racial classifications in the1770s, but later extended it to five.
Along with other general theories throughout Christian Europe, some of these classifications would likely have been agreed with by some Christians of the time. However they did not represent a specifically Christian viewpoint.