The oroblem with non-whites not quite fitting in is real, though, and much worse than in the US. Besides color, muslims are pretty hard to assimilate, so there will be not only color-based racism but also cultural ethnocentrism.
Imagine you have the problems of economic class and then add another dimension of cultural class. Society becomes much more fragmented. The new dimension is not really worse than economic class, but class alone is already unpleasant. It will turn out all right, I guess, but there will be minor persistent problems for a long time.
To be honest, I think you may have read too much Mark Steyn. There is little cause for demographic apocalyptics, including the tired "Muslims are going to revolt/take over" kind. In fact, a flat or slightly declining population is probably a blessing (e.g. from an environmental perspective).