The myth they seem to be debunking is that Europe was >99% white. But what if the claim is that it was only as white as, lets say, before WWII? It would be mighty strange if Europe was at its historically unique least diverse right at the point where we start having photographic evidence.
It would be kind of crazy if visible ethnic diversity didn't drop consistently generation after generation after the Roman empire moved east, but especially between 1200 and 1700 given waves of xenophobic hate, evictions of the moors and paranoia that anyone with the potential for external connections, (such as connections with the newer hubs of international trade) was poisoning wells.
Of course. When it comes to debunking claims of a white Europe, medieval people didn't think of race as we do today, and their cities were centers of trade and multiculturalism. But when it's time to explain the documented homogeneity at the start of the 20th century, they turn into racist xenophobes, whose ideas of race match present-day ones.
But I will grant you that the reconquest of Spain from the Moorish invaders probably did reduce the diversity of Spain. I guess the native Spaniards didn't appreciate their new rulers? Though it's strange to call a massive military effort against one of the largest colonial empires at the time an "eviction".
I don't really get your first paragraph. Medieval people fought about religion and religion usually correlated to origin. I.e. the Sicilians integrated with the portion of Moors that converted.