When people -- myself included -- say they have a problem with chemicals in food, they of course mean artificial chemicals: that is, compounds, preservatives, dyes, and flavors that are non-naturally present for that particular food item and were added for their shelf life, taste, aesthetic, or addictive properties.
Next time you visit your grocery store, go read the ingredients list of a few different boxed and frozen items. It's not uncommon to see three- or four- dozen ingredients on items that should have less than 10.
While all of these compounds may have FDA approval and studies verifying their safety for ingestion, please keep several things in mind:
1. Studies use large, population-based sample sizes and their effects are based on their statistical significance on these populations. In other words, "side effects" are a population-level phenomenon, not an individual phenomenon. It is plausible that individual side effects are hidden as statistical noise. This is a problem with pharmacological studies as well and there is no easy solution to it AFAIK.
2. We have a massive obesity crisis in this country (and increasingly globally). Sedentary lifestyles and increased caloric intake is no doubt part of this, but it is blindingly obvious (to me, at least) that the meat of the problem is environmental, primarily diets, and these compounds are wreaking havoc on the endocrine systems of the population causing a massive uptick in obesity and diabetes.