I haven't read much from Reich, so I don't know his position. But I've understood that the current best practice in human genetics is to explicitly justify the population descriptors chosen for each study, rather than using any fixed set of descriptors given from the outside.

There are two main types of genetic descriptors: those based on genetic similarity and those based on ancestry groups. Genetic similarity is quantitative, and individual samples often have multiple labels attached to them. Ancestry groups are discrete categories based on quantitative measures. If it's appropriate to use descriptors based on genetic ancestry groups in a study, it's usually also appropriate to drop samples that don't fit neatly in any single group.

Sometimes it's more appropriate to use descriptors based on environmental factors, such as ethnicity or geography. Environmental descriptors tend to be correlated with genetic descriptors, but they are not the same.