Hmm well I think my impression has always been that in the US, soc and anthro have different intellectual lineages, methodologies, and particular histories. soc in the us tends to be more conservative theoretically and politically and to utilize quantitative, demography and statistical analyses far more frequently than anthro or sociology in other countries. anthro in the us tends to be pretty up straight qualitative and ethnographic.
one thing that ive noticed is the difference in how scholars and students describe their interests between anthro and soc. sociologists tend to list their sub-disciplinary allegiances e.g. "medical sociology, sociology of the body, critical race studies" where as anthropologists tend to list things like "subjectivities, politics of representation, US, Latin America" or one particular aspect of something- which falls under a subdiscipline of anthro but gets presented differently. Soc in the US is often preoccupied with policing the boundaries of subdisciplines and what counts as sociological knowledge. Largely because sociology doubled down on being scientistic because of institutional crises and works hard to pass as legitimate above all else, to the detriment, I would argue, of interesting, critical scholarship.
abroad, at least in europe, sociology has far stronger ties to things such as critical theory (for lack of better term), cultural studies, media studies, etc and I think theres a lot more resonance with anthro as a result. not that theres not room for these things in the US but its a matter of finding good pockets in which to do this.
you shouldnt really have a problem doing political economic work on South Asia, I shouldnt think. You might have to dance at certain points to make things "count" (often literally) but you should be fine. Can't speak to UMinn in particular tho.