I believe multiculturalism can only thrive when people fully immerse themselves in the culture of their new homeland.
My grandparents immigrated from a Commonwealth country in the 1950s, making me a second-generation immigrant. Despite not being white, I identify strongly as British, or perhaps English. I speak the same way and engage in the same activities as my white friends. I even married a white woman.
However, I do agree with many of your points about the impact of the area on multicultural integration.
Initially, we lived in a diverse neighborhood with a mix of Whites, Blacks, Indians, and Pakistanis. I noticed that Indians and Blacks integrated well, while Pakistanis tended to keep to themselves, leading to some tension between the Indian and Pakistani communities.
When my parents moved to a nicer area, the demographic was still diverse but predominantly white, and everyone got along much better.