Almost like Apple with component serialisation.
1. Bacteria
2. Parasites
3. Cancer
In all these cases cells that are "other than your own" are in your system and need to be eliminated, in the case of cancer it's your own cells but with significant mutations, as far as I can tell there is always an immune response although in some cases it is actually counter productive.
Even if we assume your body has a foolproof is_same_species() test, your neighbors' cells may:
1. Be healthy, but have the wrong priorities or behavior, so that they start doing the wrong tasks or sending the wrong messages in the wrong places. [0]
2. Be healthy, but they're just a creepy flesh-mask a parasite has constructed around itself.
3. Be individually hijacked by viruses, and your body won't have the same baseline information to tell that they've deviated from your neighbor's standard.
4. They may be fully human, but gone feral into a transmissible tumor [1].
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[0] This is actually a risk from pregnancy, as overambitious fetal cells leak into the mother.
[1] https://en.wikipedia.org/wiki/Clonally_transmissible_cancer
The reason I needed a kidney transplant is because of an auto disease called IgA Nephropathy where the IgA antibody has a small defect that causes the rest of the immune system to attack it and the whole mess clogs up the kidney filters over time.