I think it depends on whether you really, really object to dying of certain things, to the point that you are prepared to take substantially elevated risks of dying of B in order to avoid dying from A. People are terrible judges of risk, even without the media shouting at them.
For example, when many Americans stopped flying after 9/11, an
additional 1,200 people were killed in the resulting increased road traffic and consequent collisions. But of course, those road deaths were not on the news for hours on end, in slow-motion, with endless talking heads.
Nuclear energy cannot compete if it is held up to impossibly high safety standards. The standards are already very, very high, comparable to the airline industry (in which analogy, the coal-fired energy producers are working to automotive safety standards). And of course, there's the paradox that the safer things become, the rarer the incidents, and so the greater the media impact of each incident. (If we'd been having a minor radiation leak every 3 months since the 1950s, we probably wouldn't even be having this debate.)
My advice to people who are still worried would be to inform yourself: about the real effects of different doses of radiation, about the actual chances of you being exposed to those doses, about the massively higher chances of many other bad things happening you in the next X years, and about very large and very small numbers in general (
this is a good source). But "we don't know everything, it's scary, something bad might happen" is not a good basis for public policy discussion when it comes to something as fundamental as energy supply. Governments and/or corporations don't build nuclear plants for the fun of it.