"White people" as such aren't an ethnic group. There are a large number of ethnic groups made up of "white" people, and at times relations between them can be very hairy indeed. (Think of the former Yugoslavia, for example, or Northern Ireland.)

In North America, for example, my understanding is that "Anglos" and "Hispanics" tend to be regarded and to regard themselves as belonging to different ethnic groups, even when the individuals concerned may both be "white".

This isn't just me being pedantic. It illustrates how variable and arbitrary are the ways in which we divide ourselves up.