The article that is provided states that inherently microwaves do not cause cancer, but that plastic exposed to radiation may stem carcinogens, which can cause cancer through DNA manipulation. Furthermore, it is provided by the FDA in the article that even small accidental radiation energy outside of a microwave is way below the level that is harmful to humans.
According to information published by the Food and Drug Administration (FDA), microwaves are non-ionizing radiation, which means that it does not pose the same threat as x-rays or other machines. Microwaves are categorized as “electromagnetic” radiation, which means there are waves of electrical and magnetic energy moving in space at the same time. This energy is the same radiation in radios and short gamma rays, which further prove the low risk to human contact. The only time where radiation is dangerous, is if it is classified as ionized. Ionized radiation has the power to knock electrons out of atoms and molecules which can alter cells in organic matter. X-rays are a type of ionized radiation, which is why some may get confused in thinking that microwaves are as well.
While microwaves do not cause cancer, exposure to high level microwave radiation can cause burns on the skin through heating of the body tissue. Additionally, the eye may be a vulnerable location to intense heat, and may lead to cataracts if microwave radiation and heat is sufficient enough. However, these are very rare cases, and would only result from lack of knowledge with this cooking and heating tool.
https://www.fda.gov/radiation-emitting-products/resources-you-radiation-emitting-products/microwave-ovens
The only evidence that I could find that undermines my claim, is from an article published by the National Library of Medicine. This short article states that “long-exposure to low-intensity microwave radiation may have carcinogenic (cancer-causing) effects” (I Yakymenko 1, E Sidorik, S Kyrylenko, V Chekhun). The researchers found that during an experiment with rodent exposure to microwave radiation, there was a significant rise in cancer rates after 17-24 months. These cancerous signs include overproduction of reactive oxygen species, DNA damage, and activation of enzymes which supports tumor growth. This article seems to take a very aggressive stance on microwaves, and seeks to debunk the general paradigm on the safety of the machine.
https://pubmed.ncbi.nlm.nih.gov/21716201/
Yet, while this information seems worthwhile to dive into, there is just not enough supportive evidence and findings to make the claim that microwaves cause cancer.