Not sure which “stem cells” you mean, but I think the recipient’s immune cells colonize the graft. Which means they’d start attacking the original donor(graft versus host disease in reverse).
But you’re probably correct that the immune cells transferred would also be the same problem. But that’s what anti rejection drugs are meant to deal with, aren’t they?
Assuming two people have the same blood type, I believe the compatibility factors are reciprocal between two people, aren’t they? So if you and I are compatible, and of the same level of health, then if we swapped kidneys we should each have about the same risk factors for rejection.
But if as some people were asking, we took a transplanted organ and transplanted again, the compatibilities are not reciprocal any more, and I would not be surprised if you had to assay all three people to figure out the compatibility of the organ. Since it’s my tissue (and perhaps a bit of yours), your T cells, and the recipient’s immune system all having to get along, at least until your immune cells age out, and perhaps longer if the organ is chimeric.
It’s true that some stem cells leave their niche, HSCs can be found in circulation.
To your question about two people swapping kidneys, I’m not so sure. I think that depends on the T cell repertoire, and there’s a lot of variability depending on the life history. So, person A getting a graft from person B might not get the same reaction as person B getting a graft from person A.
