I think you sum it up quite well. As a European, I support this stance, but encounter resistance from most Americans when it's discussed (even the more liberal ones) because it's such a culture shock.

I don't know if it's related but I travel in the US quite a lot and notice that compared to the UK, at least, races and cultures tend to separate themselves a lot, whereas even in rural areas of the UK, people integrate a lot more and seem to care less about race or culture.

Radical Islamist and far-right groups are constantly looking to provoke anger and dischord, with regular demonstrations and counter-demonstrations by groups like Islam4UK and the English Defence League posing a real threat to civil society.

Sort of, but I'm not entirely convinced these groups are any worse than many right wing groups in the US who protest against gay marriage, the welfare state, or abortion. We merely see them as being radical because of our laws whereas in the US, a group like the EDL wouldn't be seen as particularly interesting.