I dug into this quite a bit a few years ago and came to the conclusion that opposition to nuclear power was originally all astroturfed, and continues to be astroturfed to this day. I may have missed something and I don't know why leftists in particular are against it, but here's what I learned.
Environmentalist organizations were for nuclear power into the 1960s. In general people were for it, it was a promising new technology. Then in the late 60s and early 70s these big environmentalist groups (Sierra Club primarily, but others as well) were taken over and astroturfed by oil and gas companies. Obviously oil and gas capitalists were not at all on board with the idea of getting plentiful and cheap energy from little bits of metal, so nuclear energy had to go.
At the same time there was a huge anti-war and anti-nuclear weapons movement. It was super easy for bad faith actors to conflate nuclear weapons with nuclear power, and that's one of the anti-nuclear-power misconceptions to this day. There also wasn't any public awareness or even concept of climate change and greenhouse gas emissions.
In the 70s public opinion shifted hard against nuclear power, first due to these oil and gas lobby efforts and later due to opportunistic propaganda around the Three Mile Island accident (and the conveniently released film The China Syndrome). Further accidents such as Chernobyl (and its easy conflation with anti-communism) have only served to make nuclear less and less popular over the years.