Above is a composite of some of the depictions of Jesus Christ throughout the years and throughout the cultures. There are many more, like an Indian Jesus being crucified that’s blue and whatnot. Cultures depict Jesus in a way that makes the most sense to them. Western culture, which originated from Europe, is overwhelmingly white, so… white Jesus. We just aren’t as exposed to other depictions of Jesus around the world because we don’t live there. What Jesus looks like is not as important to Christians as who Jesus is, however. In every culture, Jesus is the one who sacrifices, who suffers all for the sake of ultimate love for all. A God who dies is not accepted in many cultures (we struggle with it, too), but an innocent person who is about love and forgiveness who is unjustly condemned to death, murdered horrifically, but triumphantly breaks the shackles of death through resurrection, every culture pays attention to that! Both are true, however.
Since Jesus did this for all people, he can be Indian to an Indian person, European to a European person, African to an African person, etc. What Jesus does defines who Jesus is, so looks become less important. I think Jesus came at a time when he couldn’t be easily depicted so that it didn’t get in the way of accepting what He has done for all of creation. People are shallow. Can you imagine if people today would reject Jesus and the Gospel because they saw a picture of Jesus and thought He was ugly? It’s sad, but many probably would do just that.