Nothing man-made is perfect, not even nuclear. But even with the two big accidents, nuclear is the safest form of energy generation we have. By far.
The actual safety is almost entirely unrelated to the fears people have. There is even a term for this: radiophobia.
https://en.wikipedia.org/wiki/Radiophobia
Radiophobia is an irrational or excessive fear of ionizing radiation, leading to overestimating the health risks of radiation compared to other risks. It can impede rational decision-making and contribute to counter-productive behavior and policies.
I think the concern most people have is not necessarily the long-term health effects of nuclear vs other forms of power, but the risks of a catastrophic incident