The U.S. has done a pretty reliable job recognizing and regulating threats to our health. A system of 300 million people certainly doesn't move fast - and it's easy to point out scandals and tragedies that have occurred between recognition and regulation - but overall America's a pretty safe place to live.
Pesticide regulation is a good example of this familiar arc. Following some initial faltering in the mid-20th century, a comprehensive system of regulation was developed. This system is coordinated by the EPA, FDA and USDA, and independently regulates every combination of pesticide formulation and crop. Pesticide levels and application timing are set to assure that residue levels are many times lower than have been estimated to have any detectable biological effect on humans. The EPA has an outstanding website that puts their rationale where their registrations are. Here, for example, are the toxicology results for glyphosate (Roundup).
A healthy skepticism of any governmental, corporate or non-governmental organization plays a critical role in responsible citizenship, but it's important to keep things in perspective. It seems pretty irrational to me to trust vehicle safety standards, building codes, medical regulations and educational standards - but then spurn agricultural regulations. There are plenty of countries where you can't even mail a letter confidently - but the U.S. isn't one of them.
Free countries will always have a fringe who (legitimately or illegitimately) distrust the government, whether they're libertarians, militia survivalists or conspiracy theorists. Organic advocates are entitled to view the government (and farmers) as fundamentally untrustworthy, but they should acknowledge the radical nature of that decision.