omg it is dangerous when people don't know science and use pseudo science to make an educated guess.. do you even know what non-ionizing radiation is???
they're the totally safe non radical producing energy, any invisible heat or even fire or fm radio is considered non-ionizing radiation.. please stop your ignorant fear mongering from just getting excited by key words in scientific terminology. radiation in physics strictly means the measure of frequency not radioactivity which is totally different ball game and at the extreme end of the spectrum.
and here's the hint EVERY type of cooking changes chemical structure. the basis of a chemical reaction is conversion of energy. either energy is needed or given off in order for it to take place.. this is why your food changes or 'cooks' when you heat it.
and your same Wikipedia source tells me
Microwaves do not contain sufficient energy to chemically change substances by ionization, and so are an example of nonionizing radiation. The word "radiation" refers to the fact that energy can radiate. The term in this context is not to be confused with radioactivity. It has not been shown conclusively that microwaves (or other nonionizing electromagnetic radiation) have significant adverse biological effects at low levels. Some but not all studies suggest that long-term exposure may have a carcinogenic effect. This is separate from the risks associated with very high intensity exposure, which can cause heating and burns like any heat source, and not a unique property of microwaves specifically.
By your logic we should be more carcinogenic if we heat food on a bonfire because fire is much much much more higher in the 'radiation' frequency that you are so scared about.
but honestly I don't source my arguments from Wikipedia, I actually studied science.