The plants that are already built are the problem. There are many passive-safety measures that have been devised since these plants were constructed, but since the old reactor designs are already there, people keep using them to be cheap. The difference is in when something goes wrong you can either have a reaction that halts right away or a situation like Chernobyl, Three Mile Island, or Fukushima.
Thorium reactors are pretty interesting in concept. I'd rather have a few of those around over the 35+ year old reactors we have running now. The science there is good. It's better than what we have and would be progress. That said, I understand the position against nuclear. Any time radioactive substances are being produced, there is a nonzero chance of them being spread out over the landscape.
From what I can tell, the Green party seems to be against gambling with worst-case scenarios, even if the odds of the worst-case scenario happening are remote. Let's think of a list of the worst case scenarios of things!
* Photovoltaics -- take up farmland?
* Turbines -- kill birds/fish
* Fossil Fuels -- Turn Earth into Venus
* Nuclear Reactors -- Godzilla
* GMOs -- Monsanto finishes the transition to Weyland-Yutani. Also the death of bees.
* Water Fluoridation -- Mind control!