When found, pesticide residues were similarly low in organic and conventional produce, but there is some evidence that even very low doses of pesticides might still elicit physiological effects.  These effects, be they beneficial, neutral, or harmful, and be they from organic or conventional pesticides, are not well studied. So, what is a consumer to do? The practical solution is quite simple: rinsing, peeling when possible, and cooking can reduce the amount of pesticide left on your produce, whether this produce is organic or not.  
Do you accumulate toxins?
Such programs can claim to cleanse your whole body or specific organs. They commonly consist of a highly restrictive diet, with a possible array of supplements. The Master Cleanse, for example, prescribes 6–12 glasses of lemonade with maple syrup and cayenne pepper as your only sustenance. According to its creator, this program promotes “the elimination of every kind of disease” and is the most successful healing diet in the world.
(Alas, organic products are not unilaterally safer than conventional ones: a 2018 test of protein powders revealed that organic ones had about half the amount of BPA (an industrial chemical) but twice the amount of heavy metals.)
Standard medical detoxification involves shoving 25–100 grams of activated charcoal down your throat every couple of hours to prevent the swallowed chemicals from being absorbed from your gut into your bloodstream.   The charcoal binds the chemicals, allowing you to poop them out.
Detoxing done right.
While the USDA does not currently test for residues of pesticides commonly used on organic foods, it does test for residues of pesticides not approved and some approved for limited application. Unsurprisingly, organic produce (notably fruit) less often have synthetic pesticide residue than conventional produce do.  Trials in adults and children have shown that switching from conventional to organic produce can reduce biomarkers of organophosphate-class pesticides, which are used in conventional agriculture and may be harmful, in as little as a week.   Fortunately, in the US, this class of pesticide has consistently dropped from use in favor of less acutely toxic ones since 2000.
So when people feel better from a cleanse, is it just a placebo effect? Not always. People who undergo a cleanse might also feel better because they stop consuming foods that don’t agree with them. In other words, cleanses work as de facto elimination diets.