https://www.npr.org/sections/thesalt/2014/06/03/318241738/ho...
Of-course there were radionuclides in our bodies even before the first nuclear test in 1945. For example Potassium-40 or Carbon-14. The presence of Carbon-14 in organic matter is the basis of the radiocarbon dating method to date archaeological, geological and hydrogeological samples.
The big question is how much radionuclides is safe and how much radionuclides is a health risk.
https://en.wikipedia.org/wiki/Dose%E2%80%93response_relation...
For a long time there was a serious debate over whether wild animals actually experienced aging or not, because they’d never live long enough to get noticeably aged.