Because of the nature of nuclear radiation, including Xrays and cosmic radiation as well, Earth is already being irradiated everywhere from every bit of irradiated material (waste) as well as the fission products themselves (the fuel that is in use). Radiation is everywhere and always. The point is that with decreased time spent in proximity to points of strong radiation, increased distance from points of strong radiation and increased shielding from those points, radiation can be, and is being, minimized.
That’s why “normal background radiation” from all sources: naturally occurring radiation in stone, coal, cement and man-made sources (including power plants), plus cosmic radiation that even penetrates thick layers of earth to deep below ground, is measured at a bit less than ~2 millirem per hour. That is, “uncontrolled background” is not a zero level of radiation, but always accounts for “some” radiation that is inescapable.
For that reason, the areas around nuclear power plants, weapons facilities, spent fuel processing facilities, high-level and low-level radioactive waste storage facilities, and the areas near non-destructive radiographic testing (that is, essentially, a type of weld inspection using radiation sources to penetrate weldments and pipe to produce images on film, among other uses), dental and medical Xray sources, medical treatment centers and all other known and controlled uses and point sources of radiation are monitored to ensure that public exposure to radiation will not exceed that figure of 2 mr per hour at any time. And those measurements are rigorous, continuous and strictly enforced.
However, that’s not to say that you cannot exceed that kind of exposure, because it’s pretty easy to do that.
If you live on top of a high mountain, in proximity to a coal mine or coal storage yard, work or live in a building made primarily of concrete, live over or near a granite outcropping or frequently fly, then your exposure almost certainly exceeds that 2 mr per hour exposure. But that’s because those other sources of radiation are uncontrolled. In fact, for the most part they cannot be controlled. (Try to imagine a scenario that protects against exposure to rock, when you live near it, or exposure against cosmic radiation from space.) It would be hard to live in any human society we’ve yet envisioned that could “protect us” from the things we’ve always been exposed to.
So, the question ought to be, “Can we adequately protect ourselves from the hazards of high-level radiation exposure?” And the answer seems to be, “So far, so good.” And there’s no indication that we’ll lose that ability.
Here are some facts about nuclear radiation, as I learned them in 1980 (and which haven’t changed a great deal since then, although the units of measurement have changed):
At 2 mr / hour x 24 hours / day x 365 days / year your permitted exposure as a member of the public living or working in or near “uncontrolled” areas adjacent to a nuclear power plant (or any of the other point sources I noted earlier) would be around 17.5 Rem per year. That’s “uncontrolled” – no one is going to check on or be at all concerned about a person receiving that much exposure per year.
The reason no one will be concerned about that is because at exposures of 25 Rem or less, no one has ever been able to demonstrate harm. (There have been hypotheses that a certain amount of regular low-level exposure such as that is actually beneficial, but I don’t know what has become of those hypotheses.) The NRC (Nuclear Regulatory Commission of the USA has determined that in addition to the ‘normal uncontrolled background’ radiation, “nuclear workers”, that is, those who work with exposures to radiation in controlled areas (that is, any of the areas noted above where exposures can exceed the 2 mr / hour rate in controlled areas) may not receive more than 5 Rem of exposure from those controlled sources. And you would have to see the record-keeping and monitoring that goes on to ensure that those levels are not exceeded; those workers are kept under tight supervision to stay well within those limits.
In short, the dangers of radiation exposure from controlled sources are minimal. It’s true that most industrial sources of radioactivity are long-lived, so they need to be controlled for many centuries to ensure that these exposures are kept “as low as reasonably achievable” (ALARA) in perpetuity, and of course, kept from groundwater and other places where the radioactive materials can be spread (and certainly, away from groups of people who would do harm with them), but that’s not a technological problem so much as a sociological one.