There are plenty of people who are Born here who have radically different cultures to other people who are born here and it seems to work ok.
Overall, yes, but my region has seen a lot of incidents that should make us all pause for thought.
One kurdish asylum seeker in his mid 20s was brutally attacked and left with serious brain damage because he was perceived to be "anti-Saddam" by the "pro-Saddam" community around him (who incidentally were neither Kurdish nor Arab). We have had running street battles between EU nationals and other migrant communities in some areas.
I think there is a great danger in only seeing the challenges of multiculturalism through white, British, middle-class eyes, and being blind to the faultlines between non-English-origin communities themselves.