Basically, there is lot of empirical data which can be described by a linear relationship. Of course, if you go to even lower doses then the effect size becomes smaller and it becomes harder to show this effect in epidemiological studies. But large scale studies show that even for the rather low doses from medical imaging, the data is consistent with this model (e.g. Pearce et al., Lancet 2012;380:499–505). A lot of effort therefor goes into reducing radiation from medical imaging. Conceptually, we assume that there has to be some tiny risk with any damage caused by ionizing radiation because physiological repair mechanisms can not be assumed to be perfect. So the assumption that additional radiation (there is always a background) causes a linear increase of risk is natural. It is, of course, possible that additional effects can cause some nonlinear effects, e.g. additional repair mechanism get activated at some dose or repair gets overwhelmed at some point. But something like this would not really be expected at extremely low dose close to background levels. It is also not clear whether such an effect would lead to a lower or higher risk estimate for low doses.

Finally, one can also observe that some of the most prominent critics of LNT are connected to industry lobbyism. We have seen this before also in the tobacco industry who downplayed the risk of smoking, sometimes even the same persons appear in this context. Terminology such such "LNT worshipping" is a clear tell sign where this is coming from. Similar to all pseudoscience it has to come with a theory how established science is wrong because scientists are stupid, corrupt, worshipping some dogma, etc.