Anthropologists had previously distinguished between "biological kinship" and "social kinship" (Hawkes, 1983) or between "natural kin" and "nurtural kin" (Watson, 1983) - but they mostly lacked a coherent theory about the evolutionary basis of these categories. Cultural kin selection helps to explain why these traditional anthropological categories are as useful as they are.
However, anthropologists essentially failed to discover cultural kin selection. This was probably largely because of their widespread rejection of cultural evolution - apparently due to fears about eugenics and the like. Scientifically speaking, this was an even bigger mistake.
As a result, attitudes towards cultural kinship within anthropology went in other directions. Anthropologists often seem to see "social kinship" as one of the key reasons for not applying Darwinism to humans. By contrast, in memetics, cultural kin selection is one of the centre pieces of applying Darwinian evolutionary theory to humans. To illustrate the anthropological perspective, here is a quote from Dwight Read's The Evolution of Cultural Kinship: A Non-Darwinian Odyssey:
I take up the question of whether or not the evolution of human societies and cultural systems from a non-human primate ancestor can be accommodated within a Darwinian framework for evolution. I assume that for a non-human primate species, its social structure, form of social organization and kinds of social behavior evolved through Darwinian processes such as biological kin selection, inclusive fitness, reciprocal altruism between biological kin, and so on, including direct phenotypic transmittal of behavioral traits viewed as part of the phenotype of an individual organism. The fundamental question being addressed, then, is whether or not we can embed the evolution of human social and cultural systems within this framework and the conclusion I reach is that the evolution of human social and cultural systems cannot be adequately embedded within this biological framework for the evolution of social systems.
It seems evident that one side of this debate is sorely mistaken. In general, it appears that most of the anthropologists involved are not properly aware of cultural evolution - and their reasoning about Darwinism falls apart at that point. An understanding of memes changes everything.