Furthermore, even if we ignore the above reservations we find that ethnicity/culture/religion doesn't account for much. So when someone says that group X is more likely than group Y to be racist, for example, it doesn't mean that all of group X are racist and none of group Y are. Indeed, the group differences are often very small indeed, and are subsumed by the differences within these groups. What statisticians would call 'unexplained variation' is very high, and it is often assumed that there are other things at play that we don't or can't know about. It seems obvious that these things will include personality, as how someone approaches life will have a bearing on how life plays out, and individual circumstances, and here I'm interested in this with regards to migrant 'integration'.
There is psychological work on this, under the rubric of 'acculturation' (although I haven't found any from the UK), but, as ever, sociologists don't engage with it and vice versa. Furthermore, one critique I'd have, is that the psychological work seems to assume that the migrant unproblematically brings a culture with them, fully formed (see Chirkov 2009 for a similar argument). Thinking about what I would be like (hypothetically) as a migrant, though, it's not so clear cut: some things I'd take with me (drinking tea with milk, and bitter) and others I may well deliberately try to change, depending on where I was going (social formality - i.e. the kind of English awkwardness that means we don't know whether to shake hands or just to nod hello). It's anecdotal evidence I have here, but I'd wager that personality or outlook has more of an impact than 'ethnic' or religious background...
I live in a place where migrant integration comes easily. There's none of the poverty and disenfranchisement that can set people up against each other, regardless of background. Nor are there any of the geographic processes - white flight, self-segregation or rapid change - which can end up with separation by distance and the possibility of not having the opportunity or inclination to engage with the so-called 'other'. There's little of the discomfort that comes with 'separate lives' or of one 'culture' dominating over another. But even here, some people integrate and others don't, and religious, cultural or socioeconomic factors don't explain why.
A few years ago, two new families with kids moved in. One was from Arab north Africa, the other from India. One family was Muslim - with the parents being religious - the other Hindu. Both families were in the UK for a few years for work, and in both cases it was the dad who was working (and already spoke good English) while the mum was at home with small children (and didn't speak English). The family from India had one pre-school child, while the other family had baby born while here and two older children in the early years of primary school. It may well have been this latter fact that was the most important.
For Fatima, the mother from north Africa, kids, the 'school gates' and, above all, her outgoing personality made integration happen. She spoke no English on arrival, but the children learnt very quickly, and she picked it up from them and from watching daytime TV. When her children were walking home with classmates, or playing out, she'd talk to the other parents, slowly at first, and apologetic about her English. After a while this turned into conversations about the Arab Spring, how to control boisterous 5-year-old boys, Moshi Monsters, their lifestyle back home. Having the courage, or having no say in it, she got past language barriers, and ended up hanging out with everyone else - nights in with other mums, while the dads babysat, trips to kids parties, playgrounds and so on.
The other mum, though, seemed shy. She stayed at home with the child and didn't say much beyond hello. No-one really got to know her or her bloke, and we didn't really notice when they left after a few years. By that time the child was old enough to play out, but rarely did, and the mum still didn't seem to speak much English - perhaps she lacked the confidence to use that English she had, or was just shy. She only really engaged with her family.
When Fatima and her family left we held a leaving do with food, drink, sunshine, and a dozen kids playing football. The ethno-religious/cultural models would have predicted that Fatima - religious Muslim, veiled - would have been less likely to integrate than the other mum, but that's not how it played out. Personality and life stage played a much bigger part. A long time ago, when working on ideas of social capital, I suggested a good measure would be how many people came to a person's funeral: it only works at death though, so perhaps a 'leaving do' measure can work for the living.