If anything, it will be in the groups with which many people already identify themselves primarily. In many cases, this is religion, simply because church life plays such a huge role as many peoples’ community centers. I suspect some level of rich vs. poor, because it’s in the nature of such a system for many of the rich to try to take advantage of the poor, and in the best interest of the poor to fight back. People in gangs will largely just stay that way, since they’re used to just relying on the gang. Many ethnic minorities already live in clusters and multi-generational family homes simply out of fiscal sense, and because elements of culture are always important.
So that is to say, not much change in identifying and membership.
If you’re really interested, check out Dmitri Orlov’s book Reinventing Collapse, which is about his observations about the Soviet collapse and the similarities and differences here.