From what I have looked into it over the years, and I am far from some expert, but sure, it would seem that nuclear power does need to be on the table in regards to transitioning away from fossil fuels/coal. And there is indeed a somewhat irrational free floating fear about it given the stigma of some high profile events that have happened over the course of decades which isn't helped by pop culture and fiction spreading fear of nuclear, like The China Syndrome and the recent Chernobyl docudrama.
Still...
@squeekness has a point. Nuclear still has issues in regards to any number of potential negative impacts. It does still produce unimaginable toxic byproducts, the storage and disposal of which is still often controversial if not something which itself poses risks. While there are indeed better reactor designs, nuclear plants still have by the nature of the reaction used to produce power, dangers to the general public under circumstances that while not always common are also not in the "never will happen" category. Fukushima shows that there are risks from natural disasters. And even with better designs there is still the human element to take into account that any reasonable person would see can run the gamut from graft and corruption which could lead to substandard construction or procedures (Let us not pretend that this is NOT some out there idea in regards to either the private sector or government) to malign intent such as terrorist action or just plain old human fallibility and error. There is no place where one could guarantee some kind of exemption from these kind of factors. (And I want us all to imagine the widespread adoption of nuclear power in say, China or India... You think the West has issues with corruption leading to substandard building and procedures... As the saying goes those two nations simply say "Hold My Beer".)
I'm not saying that nuclear should be banned, nor that it has no place in getting the U.S. or China out of the carbon pollution business. But downplaying the real issues in regards to risk is just as bad as being alarmist on the issue. And the real issues from cost, security, storage of waste, vulnerabilities to disasters both natural and man made and on and on are not so readily dismissed if you look at them with even a conservative eye towards their real and potential impact.
Complete antipathy to Nuclear is not being realistic about what is available to be used right now and for the foreseeable future to help the world decrease carbon emissions, which even if one thinks there has been a tipping point passed already, well, adding more doesn't help either in regards to climate change. At the same time though, uncritically embracing nuclear holds potential for disaster also. Frankly I would rather see people cautious and handle the topic with that fear in mind. One of Fear's fellow travelers is Respect. And when it comes to nuclear power of any kind if we are to harness it for our benefit as a species then we really need to respect and fear it's awesome potential.