Fear is of these things is natural, but it needs to be moderated. Specifically, it needs to be moderated against the actual danger of nuclear power plants, which is astonishingly small: the number of direct victims of nuclear power accidents is under 100, and the number of indirect victims is similarly small. This is in contrast to coal- and oil-fired power plants, which directly contribute to the deaths of over 100,000 people in India alone[1].
Nuclear power is, on face value, very scary. But it's a lot less scary than just about everything else (modulo wind and solar power) we do to generate electricity, and has far better human and environmental outcomes even in its worst cases (Chernobyl).