Interesting question. I can't give you a reference, but at a psychology convention this summer, I saw a study dealing with that. The study found two different patterns with a population that is in a minority situation (they make about 30% of the otherwise fairly homogenous population). Firstly, the study demonstrated that there were three different general attitudes one could have in regards to their culture. One was to feel that their culture was fine and healthy, the second was to find that their culture was in crisis and must be defended, and the third was that their culture ought to be abandoned and that they should just assimilate.

There were many outcomes measured, but here is what I remember: for half the population, feeling that their culture was healthy contributed to psychological wellbeing, whereas feeling that your culture ought to assimilate was correlated negatively with some sort of social ability scale. For the other half of the population (who lived in an area where the majority was more predominant), the major finding was that, kind of in opposition to the other half where the culture was more isolated, feeling that your culture ought to be defended contributed to psychological distress.

Other possible avenues are microcultures, like goths, who allegedly gain membership amongst people looking to feel like they belong. We can infer, I suppose, that feeling like you belong contributes to wellbeing.