Red blood cells may also be damaged by snps. They grow with a nucleus, they use the same rules as other cells, but they lose the nucleus later on. Mature cells have no nucleus. So they may still have defective nuclear encoded proteins etc. Then of course there is the DNA in the mitochondria. They still have that and it can also be damaged by events. Other blood cells still have their nucleus. The issue with radiation damage to genes is that every cell will be damaged differently. Its children who inherit that damage who have widespread defects. One of the best ways to think of radiation damage is as severe and ongoing poisoning. Radioactive particles/molecules can settle in and keep radiating for a long time, and with some radiactive susbstances that it would be far longer than a human lifetime before that stopped.