Now, I get the premise of this thread, and things like the association between the left and homeopathic medicine/the anti-vaccination movement are pretty clear, but let's not pretend for a minute that this is something as strongly associated with the new left as global warming is with the new right. Anti-scientific notions are fundamental to buying in to the agenda of modern neoconservatism, whereas you don't have to believe that dandelions have healing powers to think that taxes need to go up. The family values feeding frenzy variety of conservatism that defines the Republicans and an increasingly large number of right-authoritarian parties worldwide has constructed an anti-scientific reality that is wholly fundamental to justifying its policies.
As for anti-nuclear having a left-wing association, I think this'd be pretty difficult to prove. I think that the anti-nuclear interest overlaps heavily with the anti-alternative fuel interest, which is almost exclusively the domain of the right. If you include Japan, it becomes difficult to make any correlation at all between anti-nuclear (energy) beliefs and political leanings.
The other issue that I believe is more contentious than it looks is the 9/11 truther thing. It represents the problem with a one-dimensional spectrum as the association between this and libertarians is abundantly clear but saying that there's an association between it and economic viewpoints is downright nonsensical. Truthfully, I think this issue is a non-starter anyway; (correctly) believing that the government is a miserable little pile of secrets is bound to have consequences, and this is still a whole lot better than the alternative of a population that is too accepting of what the government says.
This is absolutely not true. For starters,
here's a study that puts the sweet spot at vegetarianism or pescetarian diets. I implore you to do your own research if you still don't find this convincing.