Yes, that indeed is the question, and further, in a complex animal (bird, fish, reptile, or mammal) how would the changed molecule excape destruction by the immune system?
...which has already been answered on this thread, and the answer has been known for 50+ years...
and further, in a complex animal (bird, fish, reptile, or mammal) how would the changed molecule excape destruction by the immune system?
The same way that other endogenous molecules "excape" being attacked by the immune system.
If the mutation occurs in a somatic cell, it doesn't much matter whether the immune system targets it or not. If anything, it might be best if it *did*.
If the mutation occurs in a gametic cell, then that mutation becomes inherited by every cell of the resulting offspring, and thus the offspring's immune system will simply ignore it in the same manner in which it ignores all other innate molecules.
See for example The Evolution of Improved Fitness or Evolving Immunity.