The answer is: they don't care about science in either situation, and to think otherwise is probably to kid yourself.
That said, there's basically no mechanism by which GMOs would be dangerous to human health if the final product does not contain anything unexpected under test.
None of the topics you listed have equivalent conclusive evidence to eachother. For example, the evidence to support the safety of contemporary versions of common vaccines is overwhelming; but when it comes to "organic foods", it depends entirely on the exact specifics of any individual product, from the shape and surface area of the plant, washing practices, specific tendency to absorb or repel specific chemicals (naturally or artificially present) which may not have even been applied to the land for decades (for example, arsenic-based pesticides from old cotton crops leeching into rice crops), the qualities of the soil.
Science isn't a belief, it's a method, and not all conclusions are equally conclusive.
"That said, there's basically no mechanism by which GMOs would be dangerous to human health if the final product does not contain anything unexpected under test."
There's a handful of times where my opinion on something has been flipped by a single argument that fits into a single paragraph or even sentence, and my opinion on GMOs is one of them. Nassim Taleb argues that while any given GMO product may be in fact entirely safe, that as you consider the whole line of GMOs that will be created over the next decades at an accelerating pace, the odds that at least one of them turn out to be catastrophically bad enough to entirely erase the benefits of everything else done with them goes up quite distressingly.
This makes sense of the idea that A: all current GMO foods are actually quite safe but B: it may still be a bad idea in the long run. Given that things will be GMO'd on an increasing curve as it becomes easier and easier, we've seen only a very small fraction of what will ultimately be done with the technology.
Given that humans created a poisonous potato before genetic modification, it should perhaps be considered that our society seems to have already accepted this risk.
Traditional agriculture has also produced a number of things that are non-obviously poisonous that have slowly killed lots of people over time. HFCS, tobacco, etc.
I think the key takeaway is that these aren't new or different risks. You could say the same thing about iPhone apps, pharmaceuticals, or traditionally bred plants: as you consider the whole lines of $ITEMS that will be created over the next decades at an accelerating pace, the odds that at least one of them turn out to be catastrophically bad enough to entirely erase the benefits of everything else done with them goes up quite distressingly.
Thalidomide happened. But it doesn't justify abandoning pharmaceuticals entirely. There just might be some wisdom in that.
That said, there's basically no mechanism by which GMOs would be dangerous to human health if the final product does not contain anything unexpected under test.
None of the topics you listed have equivalent conclusive evidence to eachother. For example, the evidence to support the safety of contemporary versions of common vaccines is overwhelming; but when it comes to "organic foods", it depends entirely on the exact specifics of any individual product, from the shape and surface area of the plant, washing practices, specific tendency to absorb or repel specific chemicals (naturally or artificially present) which may not have even been applied to the land for decades (for example, arsenic-based pesticides from old cotton crops leeching into rice crops), the qualities of the soil.
Science isn't a belief, it's a method, and not all conclusions are equally conclusive.