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As a scientist, articles like this bother me.
1) organic products still use fertilizers and pesticides. Organic products are not inherently safer than conventionally grown products that used synthetics
2) how much residue? The dose makes the poison. We've gotten really good at detecting really tiny amounts (ppb). Those tiny amounts often amount to nothing. If you ingest a negligible amount, nothing is going to happen - your liver and kidneys do a fine job filtering. Which brings us to point 3
3) Do they have evidence for their claims for the list of health issues? I'm highly skeptical. Just because it's on an IARC list doesn't mean that the product on the market will give you cancer (anyway, those IARC lists are garbage since they do not include how much you need to be exposed to to see a real increase in risk of getting cancer).
A friend of mine told me 23 years ago to only drink organic coffee because of the fact that the pesticides used on conventional coffee plantations are particularly onerous. This guy wasn't stupid. I've ever since bought organic coffee. I've gradually increased my organic versus conventional in terms of what I buy and lately I'm mostly organic, especially in terms of fresh produce.
Pesticides and carcinogenesis is not just a fairy tale. Organic certification does rule out at least some pesticides, maybe not all, but some, obviously. Most likely the synthetic ones.
You say: "Organic products are not inherently safer than conventionally grown products that used synthetics." I have to wonder if you are biased. I've been concerned ever since reading an eye & mind opening article entitled "Food Pollution" almost 50 years ago. The ideas in there have spread into pretty common knowledge since. Pesticides, additives, all the mumbo jumbo (the things that don't make sense to you) that you may see on the labels of processed foods you see these days. Of course, you don't see pesticides on those labels, but they are apt to be in the food you eat, at least more so if you are not buying "pesticide free," or better yet, "organic" (which is supposed to include "pesticide free" but also stipulates that chemical fertilizers are not used, as I understand it).