Coal plants reliably discharge more ionizing radiation into the atmosphere than an operating nuke plant.

The danger from both is how the fuel is obtained.

If it come out of the ground, it's radioactive. Yes, that includes well water from all sources, fossil fuels, and construction materials. Up here in the Northeast, well water has high levels of uranium and radon, and frequently, thorium too.

The well water on our land is unacceptably high in all three, which is why we harvest rainwater, and use charcoal to get the mercury out.