I reckon we'd all be surprised by how many people are killed by a lifetime of shaking hands under a linear no-threshold hypothesis applied to Newtonian force.
I really don't understand how anyone can bring that model up seriously without adding in "and this highly unusual choice of model is justified by ...". It is an extraordinary claim in my book.
At a lower level their are many systems that both cause and reduce the risks of cancer. However, over a lifetime the odds of getting cancer end up being fairly high and most people end up a single mutation away from cancer. At which point every even is just another roll of the dice.
Net result, observed results look rather linear.
1) A slap on the wrist is highly energetic, and speaking from an understanding of basic materials physics it seems very likely that it damages cells, ligaments and bones. We just heal from it very easily because the damage is completely trivial.
2) Skin cancer can't be reasonable proxy. I live in Australia, and it is well-known here that skin cancer is frequently caused by sunlight.
Now the dose of radiation you get from sunlight is huge. On a typical day, you are exposed to enough radiation that you can detect it as heat (ie, we associate heat with sunlight). I've only ever been exposed to enough artificial radiation to feel heat in dental X-Rays. The LNT model is going to be operating at much lower levels, because the theoretical damage is being done to people who cannot detect it.
That link alone is surely going to overwhelm the effect of tiny doses of radiation and make it impossible to detect low-threshold increases.
1) Cells are elastic and suspended in water which allows them to survive what you might think of as extreme trauma. (Ever seen someone hammer a nail with a glass bottle filled with water?) Combine that with the elastic nature of connective tissue is what allows you to for example jump without killing off of the cells at the bottom of your feet.
2) Sunlight is EM radiation like X-Rays. However, the vast majority of the energy is harmless and and even UVA / UVB is limited to the top layers of skin. But, as far as those top few layers of skin are concerned it's like your constantly getting very weak X-Ray when standing in sunlight making it a great proxy for low level radiation exposure.
The tiny sliver of red UV that reaches past the atmosphere is what you care about. Dead skin cells block even more, but the tiny fraction of a fraction of energy can still kill you. https://en.wikipedia.org/wiki/Sunlight#/media/File:Solar_spe...
Is there any real evidence showing LNT is wrong?
There's also a chance that it'll have consequences that save your life -- e.g., making congestive heart failure a little bit less likely.
It seems uncontroversial that there may be nonlinear effects at large doses -- after all, if some dose is large enough that it almost certainly kills you then it's simply not possible for twice the dose to be twice as likely to kill you. But surely the estimates you're concerned about are not obtained by linear extrapolation from such large doses; they're the result of extrapolating from known statistics for doses small enough to be unlikely to kill, but not so small that the risk can't be measured because it's overwhelmed by background noise.
Those extrapolations could still be wrong, of course. But comparing against something that's obviously wrong like going from 100 aspirins to 1 aspirin is not a fair comparison, and scores much better on rhetorical effect than on actual evidential force.