Well if anything, immigrants, who choose to move their whole lives to Britain, should love Britain and its traditions even more than random British folks who happen to be born there.
Being brought up in a certain culture is a pretty powerful influence on who you are and what you like.
And people who choose to immigrate to a country may do so for a variety of reasons; I know a number of anglophones who hate living in Germany and are only here because of work.
I don't think that's true at all. I suspect the vast majority of people emigrate for economic reasons, not because they like another country's traditions.
