Radiophobia has roots in the fear of nuclear weapons, but has been significantly reinforced and inflamed by accidents at nuclear power plants.

Modern environmentalism was founded on fear of radioactive fallout from atmospheric testing of such weapons. A whole generation was raised on movies and literature and other art depicting nuclear radiation as the ultimate monster of modern technology.

 In the book Radiation, Pollution and Radiophobia (https://atomicinsights.com/wp-content/uploads/App-A-from-Nuclear-Shadowboxing.pdf ) there is a list of factors that have helped create of sustain radiophobia:

- government insensitivity in testing nuclear weapons in the air, underground, above ground and at sea;

- emotional impact from using atomic bombs over Hiroshima and Nagasaki;

- excesses of the Cold War nuclear-arms race and the accompanying psychological warfare;

- demonstrably false projections of casualties made after the Three Mile Island and Chernobyl-reactor accidents;

- negative lobbying by fossil-fuel industries;

- crass interests of radiation researchers for recognition and budget allocations;

- self-serving politicians using radiophobia as a weapon in seeking power;

- misleading “dirty bomb” scares by careless analysts;

- public fear induced by news media that profit by hyping news;

- counterproductive interests of “greens” (psuedo-environmentalists) who thrive by scaring the public; and

- undue complacency and laxity within the nuclear industry.

Radiophobia has roots in the fear of nuclear weapons, but has been significantly reinforced and inflamed by accidents at nuclear power plants.

Modern environmentalism was founded on fear of radioactive fallout from atmospheric testing of such weapons. A whole generation was raised on movies and literature and other art depicting nuclear radiation as the ultimate monster of modern technology.

 In the book Radiation, Pollution and Radiophobia (https://atomicinsights.com/wp-content/uploads/App-A-from-Nuclear-Shadowboxing.pdf ) there is a list of factors that have helped create of sustain radiophobia:

- government insensitivity in testing nuclear weapons in the air, underground, above ground and at sea;

- emotional impact from using atomic bombs over Hiroshima and Nagasaki;

- excesses of the Cold War nuclear-arms race and the accompanying psychological warfare;

- demonstrably false projections of casualties made after the Three Mile Island and Chernobyl-reactor accidents;

- negative lobbying by fossil-fuel industries;

- crass interests of radiation researchers for recognition and budget allocations;

- self-serving politicians using radiophobia as a weapon in seeking power;

- misleading “dirty bomb” scares by careless analysts;

- public fear induced by news media that profit by hyping news;

- counterproductive interests of “greens” (psuedo-environmentalists) who thrive by scaring the public; and

- undue complacency and laxity within the nuclear industry.

That is really impress, will scrutinize the link, thank you very much.

Radiophobia, also known as radiation hysteria, is a fear of radiation, such as x-rays and nuclear radiation. A specific phobia, it can result from misinformation or traumatic experiences. While there have been real mishaps involving radiation, a person with radiophobia will believe the risk is greater than it actually is. 

The word comes from the Latin word “radiatio” which means “glittering” or “shining”.

Symptoms of Radiophobia

The sufferer may avoid medical care in an effort to avoid an x-ray or claim that x-rays are dangerous, etc. 

extreme anxiety, dread

shortness of breath

rapid breathing

heart palpitation

excessive sweating

nausea

dry mouth

confusion / inability to articulate clearly

lack of focus

irritability

diarrhea

shaking

feelings of powerlessness

obsession with the subject of the phobia

fear or feelings of losing control

avoidance behavior

headaches

 During the final stage of World War II, the United States dropped nuclear weapons on the Japanese cities of Hiroshima and Nagasaki on August 6 and 9, 1945, respectively. The bombings, which killed at least 129,000 people, remain the only use of nuclear weapons for warfare in history.It is the roots of radiophobia.

Yes, of course the term "radiophobia" got its origin after the use of nuclear weapons at Nagasaki & Hiroshima in August 1945 by the self proclaimed champions of civilized world" but it got publicity(propagation) to deprive others from beneficial use of radiations, energy being the need for industrial & social sector development. They propagated radiophobia out of proportion in this regard & put forward LNT.

Here were already given some "technical" roots. However, I think, there are also some psychological roots:

Radiation can not be seen, tasted or smelled, yet (depending on what kind of radiation) it might penetrate even walls. So it  does not correspond to any experience in our everyday world. Humans tend to understimate risks that they are confronted with in everyday experience (e.g. the risk of car accidents) and to overestimate risks that are more abstract. 

A very similar thing as radiation is terrorism. If you ask people about their fears, many will name terrorism as a danger, although the number of deaths due to terroristic attacks is much lower than the number of deaths by accidents at your own home.

Another aspect is the linkage of radiation with cancer: 1. Many people die of cancer. 2. The cause of most cancers is unknown. 3. Yet, it is known that radiation can induce cancer. So even if you can't do anything against the real causes of cancers (whatever they are), you might think that you can at least avoid the one thing you know for sure it can cause cancer. 

There are many such "psychological features" that might have had some evolutionary functions. Those mechanisms are very general, and not only limitated to radiation. 

https://pdfs.semanticscholar.org/f7bd/f4dec334974af1a699dfa9d30d8b0c4cca9f.pdf

https://aeon.co/ideas/fear-of-radiation-is-more-dangerous-than-radiation-itself

http://www.agreenroadjournal.com/2014/10/radiophobia-iaea-blames-victims-for-all.html

One of the reason is poor knowledge about radioactivity, radiation and nuclear industry in general population. Since people do not understand it, they hate it and they easily get fear of it when they read some hoax. It is same like at the beginning, moreover, now, we have negative experiences with nuclear accidents and bombing/testing. Unfortunately, the issues associated with radioactivity in environment are marginalized and I am not sure if situation could change. It is radioecology which could be popular science joined together physics, biology, ecology, chemistry, geology ... and to assure people of acceptable risk of nuclear industry.