@cattleya This question comes up frequently for people with chronic health conditions that require periodic monitoring via a CT scan or x-ray. So I looked for what the cancer experts had to say, and found this from Sloan Kettering Cancer Center:
https://www.mskcc.org/news/scan-safety-radiation-reality-check
Essentially, the number crunchers say each scan, on average gives you a 1/2000 additional risk of developing cancer at some point. Compared to the risk of losing a lung, or worse, that is pretty low.

I talked to my new pulmonologist about how often my scans need to be done with stable bronchiectasis and no evidence of infection, and she prefers every 2 years because it can progress "silently" and we want to stay on top of things. (When I had an active infection, the scans were every 4 months.)

On the other hand, my cardiologist says we only need to repeat my heart CT if I get new symptoms or if the medication management stops working, as these would be clear signs of progression.

Both doctors stressed using the newest technology and techniques to minimize the amount of exposure, In fact my most recent lung CT only took 14 minutes from beginning to end, and the scanner didn't run the whole time. The tech explained how they keep updating her training with new software and positioning techniques, and that 10 years ago the same scan took over 30 minutes on a machine that used 4 times as much radiation.

So, how much is too much? Only you and the doctor can decide, but rest assured that no one orders these tests just out of curiousity.