I wouldn't necessarily call it irrational. While there are far less incidents in nuclear power, their severity and long term harm are much greater while being very hard to get back under control as we have seen in the past. I would assume many would prefer to have broken a bone a few times in their life instead of a single shot in the head. This fear is very much understandable in my opinion.

I do not mean to imply that there are less fatalities from other energy sources, especially since those harming the environment might cause the end of us all. It's much like the fear of flying, it is safer, but if something happens you cannot run nor stir to the side, you are completely of control and the outcome will be most certainly fatal.