I moved to Europe somewhat recently, and I haven't seen any tolerance or understanding: people are incredibly racist towards anyone with non-white skin, and it's socially acceptable to make snide comments about race in polite society. The U.S. (where I come from) is not exactly a pinnacle of race relations, but I was shocked by how much worse it is in Europe. There was a professor in my department of Bangladeshi heritage, and she got all sorts of weird comments. And as a CS professor, she was obviously not going about committing crimes, but rather writing research papers, but this didn't seem to matter to people.

In Denmark, at least, there's also this inaccurate perception, like what you mention, that immigrants are causing all the violence. But here we have basically two main sources of violence: biker gangs, who are mostly white, and immigrant gangs, who are mostly not. The kinds of people who vote Danske Folkeparti and are really worried about crime never seem to mention the biker gangs. Same in the UK: a huge amount of crime in the UK is caused by lower-class whites, the group sometimes derogatorily termed "chavs", and overlapping with "hooligan" culture. But you don't see the BNP complaining about them. Why? Because that's where their own members come from.

Some of my family is Greek, and there is no real tolerance there either, except from a smallish segment of left-wing internationalists. There are 2nd-generation Chinese-origin Greeks who speak perfect Greek and are generally integrated, but are still called racist names and considered "foreigners" by the Greeks who have a very ethnic view of Greekness (the majority).