They are, in fact, independent variables, or very nearly so. All combinations of the two things are possible, at least in theory. Japan, for example. The Scandinavian nations are similar. Type Two - A monoracial, multicultural society.
Obvious cases are Lebanon and the old Yugoslavia.
Nigeria, with its Christian South and Muslim North, also fits here, I believe. Type Three - A multiracial, monocultural society. The U.S. is the outstanding example, with some qualifications noted below. Type Four - A multiracial, multicultural society. Some people might say that the U.S. is closer to a type four than a type three.