'Anglo-Saxon' is also a bit suspect, because it describes people born in England to Germanic settlers, and their descendents, and ignores the considerable admixture of other europeans, notably several lines of Celt, but also Scandinavians, and locally French, Dutch, and not to forget the Angles who the country was named for. So if Anglo-Saxons have their kids in America (or anywhere else in the world) they aren't Anglo-Saxon kids, they are (whatever)-Saxon.
Makes my son a NZ-Saxon. No, wait a mo, my wife is from Yorkshire and Northumbrian stock, so she probably carries Viking blood, so.....
Naaah. Too complicated. Maybe one day it will get sorted with DNA.