Speaking as an EE, with a Masters in microelectronics technology, and a career designing chips, I can assure you that exposure of memory chips (Eprom, EEprom, and Flash) to X rays can cause the miniscule amounts of stored charge inside them to dissipate.
Potentially blanking out or just corrupting the data inside them. Firmware, custom programs etc. Even if not immediately damaged, weakened and liable to corrupt much sooner than otherwise. Why take the risk ? Why fixated on keeping your aids in during any such procedure ?
Zap such a memory chip enough, to corrupt the bootloader, and the HA manufacturer will not be able to recover it. Except maybe by de-soldering it. Which is hardly a practical possibility.
CT scans, or other significant doses from medical X rays, have the potential to zap the memory chips. Even if they don’t at first, they can weaken the charge inside, sometimes only a few electrons.
I have done that before, to blank out otherwise on-time programmable processors or memory chips. which were plastic encapsulated, not ceramic with a window in them to zap them with UV light.
MRI’s are different, no ionizing radiation but extreme magnetic and RF fields. Also very capable of destroying electronic circuitry by quite different mechanisms…
No competent radiologist would allow you anywhere near an MRI machine with hearing aids in your ears. I have had three now, and they were even concerned as to whether I might have some tattoos or even piercings (no). Apparently even some tattoo ink can heat up in that environment and cause skin burns. I do have some bits of titanium inside my ears which they knew about, and knew were not going to be a problem.
Knowing that I have also worked in an industrial environment, potentially exposed to shards of metal getting into my eyes, happened once but extracted, they were also concerned about that, as well as the fact that I eat game, shot with steel shot, some of which might still be inside my bowels. But head MRIs only, so they decided not to CT me first to look out for that.
Frankly, the HA manufacturers do know, when they caution against allowing their aids to be exposed to e.g. medical X-rays. Of which CT scans are quite a powerful variety. Why on earth would you do so, for no good reason ?
Luggage screening at airports etc. is at a far lower level, nothing too much to worry about with that.