|MLA Citation:||Bloomfield, Louis A. "Question 1516"|
How Everything Works 18 Aug 2018. 18 Aug 2018 <http://howeverythingworks.org/print1.php?QNum=1516>.
Let's start with the differences in types of radiation. Basically, anything that moves is radiation, from visible light, to ultraviolet, to X-rays, to microwaves, to alpha particles, to neutrons, and even to flying pigeons. These different radiations do different things when they hit you, particularly the pigeons. While "ionizing radiations" such as X-rays, ultraviolet, alpha particles, and neutrons usually have enough localized energy to do chemical damage to the molecules they hit, "non-ionizing radiation" such as microwaves and pigeons do not damage molecules. When you and your organic friend worry about toxic changes in food or precancerous changes in your tissue, what really worry you are molecular changes. Microwaves and pigeons don't cause those sorts of changes. Microwaves effectively heat food or tissue thermally, while pigeons bruise food or tissue on impact.
Wearing a lead apron while working around ionizing radiation makes sense, although a simple layer of fabric or sunscreen is enough to protect you from most ultraviolet. To protect yourself against pigeons, wear a helmet. And to protect yourself against microwaves, use metal. The cooking chamber of the microwave oven is a metal box (including the screened front window). So little microwave "radiation" escapes from this metal box that it's usually hard to detect, let alone cause a safety problem. There just isn't much microwave intensity coming from the oven and intensity matters. A little microwaves do nothing at all to you; in fact you emit them yourself!
If you want to detect some serious microwaves, put that microwave detector near your cellphone! The cellphone's job is to emit microwaves, right next to your ear! Before you give up on microwave ovens, you should probably give up on cellphones. That said, I think the worst danger about cellphones is driving into a pedestrian or a tree while you're under the influence of the conversation. Basically, non-ionizing radiation such as microwaves is only dangerous if it cooks you. At the intensities emitted by a cellphone next to your ear, it's possible that some minor cooking is taking place. However, the cancer risk is almost certainly nil.
Despite all this physics reality, salespeople and con artists are still more than happy to sell you protection against the dangers of modern life. I chuckle at the shields people sell to install on your cellphones to reduce their emissions of harmful radiation. The whole point of the cellphone is to emit microwave signals to the receiving tower, so if you shield it you spoil its operation! It would be like wrapping an X-ray machine in a lead box to protect the patient. Sure, the patient would be safe but the X-ray machine would barely work any more.
Returning to the microwave cooking issue, once the food comes out of the microwave oven, there are no lingering effects of its having been cooked with microwaves. There is no convincing evidence of any chemical changes in the food and certain no residual cooking microwaves around in the food. If you're worried about toxic changes to your food, avoid broiling or grilling. Those high-surface-temperature cooking techniques definitely do chemical damage to the food, making it both tasty and potentially a tiny bit toxic. One of the reasons why food cooked in the microwave oven is so bland is because those chemical changes don't happen. As a result, microwave ovens are better for reheating than for cooking.