One framework I subscribe to is like this:
Your “spirit” (here meaning your consciousness – the perspective that experiences things) isn’t your body and isn’t your ego, and experiences different lives as different people, races, genders, probably species, and also spends some time not in a body. Time may also be an illusion from a spirit perspective. The embodied ego experiences are something the spirit pays some attention to, but are not the same as the spirit.
So there’s no race to segregate by,
However, people who knew each other in one lifetime seem to frequently reincarnate and know each other again in later lifetimes.
Oh, and I think one spirit may also map to many people living at the same time.
Another framework I like (which isn’t actually incompatible with the above) says that we retain spiritual connections to our ancestors, both in life and after death. And as much as those people can be described as sharing a race, that tends to mean same-to-same “race” remains connected, even though it’s really about ancestry.