But it depends which part of Europe you are talking about. I don't think that kind of overt racism is particularly more common in Western Europe than in the US. And in the east, historically, racism against black people has not been the most problematic form of racism, simply because it remained largely theoretical. Unlike anti-Semitism or inter-ethnic hatreds.
And on a similar note, to say 'Europe is not as diverse' is a bit simplistic - because the very definition of 'diversity' depends on what you think are significant differences. Those categories are not set in stone, they are themselves socially determined. The many prejudices and antagonisms that have existed in European countries have been between groups that would not be considered different races in US terms. Anything can be viewed as diverse or not, just by changing what categories you use to decide on difference. Societies that appear homogeneous to outsiders can be massively diverse from the perspective of those within them, and can be teeming with conflict between groups as well.
Edit - in fact, at least one kind of racism seemed to be _more_ present in the US than the UK, at least for a brief period.
Namely, I remember when the Simpsons first appeared decades ago, wondering how on earth they could get away with the Apu character, who in a UK context seemed straight out of the cheap racial stereotypes of the 1970s. Letterman had a weird 'comedy south asian' guy on his show as well I recall. All of that would have seemed embarrassingly retro in a UK show (but would have fitted in perfectly to 1970s Britain).
I concluded it was just that South Asians in the US hadn't had the same rough time they had here so were more forgiving of such stuff and weren't bothered by it. But now it seems in fact it was just a question of time, as it seems the Apu character has become contentious in the US after all, just 20 years late.
Conversely, I've winced at depictions of Mexicans in the UK that would have started a storm of protest in the US, but here nobody is very conscious of 'racism against Mexicans'. It just doesn't show up on the radar of offense. It's kind of a mirror mirage of the Apu thing, really.