It's way more complicated than that. We don't know exactly how Jesus looked. We do know he was a Galilean Jew. The closest contemporary group to that of a Galilean Jew would be an Iraqi Jew. Race is complex. Many Iraqi Jews are white-passing. Even by U.S. census, they'd be classified as white. It's very possible that Jesus could have been white-passing. It's very possible he was as dark-skinned as semites come.
Regardless, to your greater point, I don't really understand. He's the son of God. Even if all Americans were vehemently racist against middle-easterners of all kinds, it's not surprising that they'd make an exception to the son of God. And honestly, this dude was born to a virgin who was impregnated by unknown means canonically. I'm sure Europeans would just retconn Jesus as being born white as a miracle of God or something.