People probably overestimate how "non-white" Jesus would be at the time. The whole skin color thing is a very colonial concept. I don't know that in a world centered in the Mediterranean people would have thought of Italians as "white" and Northern Africans or Middle Easterns as "non-white".

So in a way maybe yeah, "white Jesus" is a very American invention, just not necessarily in the way Americans parse it. US racial categories don't work anywhere else even today, anyway.