There was a useful, if short, review by David Ropeik of Harvard in Aeon a couple of weeks ago under the title “Fear of radiation is more dangerous than radiation itself“.
This is something which has been said for a long time, but it is useful to have the threads pulled together in a referenced article.
As usual I’ll give your the tl;dr version.

The fear of ionising (nuclear) radiation is deeply ingrained in the public psyche … we simply assume that any exposure to ionising radiation is dangerous. The dose doesn’t matter. The nature of the radioactive material doesn’t matter. The route of exposure – dermal, inhalation, ingestion – doesn’t matter. Radiation = Danger = Fear. Period.
The truth, however, is that the health risk posed by ionising radiation is nowhere near as great as commonly assumed. Instead, our excessive fear of radiation … does more harm to public health than ionising radiation itself. And we know all this from some of the most frightening events in modern world history: the atomic bombings of Japan, and the nuclear accidents at Chernobyl and Fukushima.
Much of what we understand about the actual biological danger of ionising radiation is based on the joint Japan-US research programme called the Life Span Study … of survivors of Hiroshima and Nagasaki [see also here]… Within 10 kilometres of the explosions, there were 86,600 survivors … and they have been followed and compared with 20,000 non-exposed Japanese. Only 563 of these atomic-bomb survivors have died prematurely of cancer caused by radiation, an increased mortality of less than 1 per cent.

Based on these findings … the lifetime cancer death toll from the Chernobyl nuclear accident might be as high as 4,000, two-thirds of 1 per cent of the 600,000 Chernobyl victims … For Fukushima, which released much less radioactive material … UNSCEAR predicts that ‘No discernible increased incidence of radiation-related health effects are expected among exposed members of the public or their descendants.’
Both nuclear accidents have demonstrated that fear of radiation causes more harm to health than radiation itself … 154,000 people in the area around the Fukushima Daiichi … were hastily evacuated. The Japan Times reported that the evacuation was so rushed that it killed 1,656 people … The earthquake and tsunami killed only 1,607 in that area.
… … …
In 2006, UNSCEAR reported: ‘The mental health impact of Chernobyl is the largest public health problem caused by the accident to date’.
… … …
Fear of radiation led Japan and Germany to close their nuclear power plants. In both nations, the use of natural gas and coal increased, raising levels of particulate pollution and greenhouse gas emissions. Neither country will meet its 2020 greenhouse gas emissions-reduction targets.
… … …
Fear of radiation has deep roots. It goes back to the use of atomic weapons, and our Cold War worry that they might be used again … Psychologically, research has found that we worry excessively about risks that we can’t detect with our own senses, risks associated with catastrophic harm or cancer, risks that are human-made rather than natural … Our fear of radiation is deep, but we should really be afraid of fear instead.

Or in the immortal words of Rear-Admiral Sir Morgan Morgan-Giles: Pro bono publico, nil bloody panico.