I suspect that primate skeletal biology is basically tantamount to studying human precursors/early cousins, i.e. australopithecines and the like. That's striaght-down-the-middle anthropology, and biologists only get involved as specialty consultants.

Things anthropologists might need to know, addition to anatomy: the chemistry of clay pots (archaeology); the metallurgy of swords or armor or jewelry (also archae); the speciation of grasses in baskets (archae, cultural anthro); climatology and geology (archae, cultural anthro, social anthro); mathematical formulas for language-change over time (linguistics, cultural anthro); brain structure and neurochemistry (linguistics); and so forth.

Sure, there are parts of anthropology that are obviously humanities-oriented; but the sciencey stuff is pretty front and center too. The fact that these differing flavors of anthro cannot live and let live is... probably inevitable and inevitably irritating.