You might be correct, regarding your comment on English. I've recently had to deal with quite a few eastern Euro pe-on types in my bidness lately. They like to play dumb, like they don't understand English...I catch'em all out by manipulating a few choice words while giving them a work description or estimate. I can tell the ones who truely do not have a grasp of English right away......the others who do understand, well, they smarten up very quickly and "remember" how to speak English almost instantaneously......it's always good for a chuckle around here.....
As far as my own personal experience goes......it is mostly non white immigrants who chose not to assimilate.
I guess it depends on where a person lives, and perception of assimilation. I know a lot of immigrants who don't want their children to assimilate into 'American culture'. My mother was much more strict about my friends because she feared me getting Americanized and hanging on the street corner, being disrespectful,etc. My father, an Ellis island immigrant, just issued death threats to the locals and when that didn't work we moved (out of Queens).
About English... you're right about that.
Sometimes I wouldn't care if some immigrants couldn't talk at all --- it's not so much what language they chose to speak but when they can't support themselves because they won't learn the language of this country and you see the very high rates of Medicaid and food stamp use, then you do mind. Also when they demand everything be provided to them in their own language they really do get annoying.