“How, then, did we end up with a white Jesus in Europe and America?”
The available actors were blue-eyed, white and blond/brown hair, IIRC.
What I have read is that there was a rather infamous Pope (Alexander VI, who had many children by his many mistresses) whose son was also rather renowned (Cesare Borgia)... Kardashians if you will... and that the Pope commissioned a painting of Jesus and his own son was used as the model in a painting many centuries ago... and it was so popular and ubiquitous that it became THE Jesus appearance to use. He happened to have flowing hair and blue eyes, and was chosen expressly because he was more European-looking.
Makes sense to me.