I'm really interested on this topic.
As you know, England was heavily a Christian country even during WW1 and WW2 - during such times, there was an Arab population in England (limited) and they faced discrimination on the basis of race.
Yet Jesus, looked closer to an Arab than he did a European. Clearly, most depictions of Jesus in the Western world resemble Europeans however reconciling the fact that Jesus was probably olive-skinned and not white is a very easy thing to do once you think about it.
Are there any accounts of how people reconciled racism towards non-Europeans with the fact that Jesus wasn't white?
I am afraid I do not have accounts as you ask, but can aid you in contextualising the question further which I hope helps.
The key period you should be looking into are between c.650AD to c.750 for context, and c.750 to c.800AD for change in imagery.
I understand that Christianity has shifting in weighting from the East (Syria, Iraq, the Byzantine Empire), to the West (modern-day Europe). The reason for this is political and religious, dating around c.650-c.720AD, whereupon Islam was founded and the culturally manifest warring culture of the likes of the Umayyad clans were captured in Islam. Raids turned to conquests as the Byzantine and Persian wars weakened the region to the north of the Arabian peninsula such that the papacy could no longer look to the Eastern Roman Empire (Byzantine Empire) for protection.
Iconoclasm in the Eastern Roman Empire (https://en.wikipedia.org/wiki/Byzantine_Iconoclasm#The_first_iconoclast_period:_730.E2.80.93787), a phenomenon which appears as a reactionary act to the cultural threat of Arabian proliferation and territorial gains, resulted in the loss of the eastern ideal of Christ. Subsequent western cultural domination (which to a more exaggerated extent exists today - please be aware of the significance of this) morphed the imaging of Christ such to find its centre in north-western Europe, most notably Frankia(/Francia) (modern-day France) under Charlemagne. He was crown Holy Roman Emperor by Pope Leo III on the 25th December 800AD; a significant factor in the shift in favour from the Byzantine East to the Frankish West.
So far as your question goes, Byzantine iconoclasm if the most relevant factor I can offer help with.
Sorry I couldn't be more helpful.