Light and heat are both results of radiation. Microwave ovens work by sending waves of energy of a certain wavelength (ie, a certain wavelength of radiation) into the cavity, bouncing it off the walls and into the food to heat it.
Servicemen working at early radar (microwave) installations would stand outside in front of the emitter before a hot date, for the microwaves to sterilise their semen production. Some later discovered that they had over-done it. Microwave ovens are now in just about every home, and the correct safety precautions when using them are common knowledge, but to begin with many people wouldn't use them at all - the radar stories still lingered.
Gas cookers used to be lethal, electricity and water can kill if they get together, and the second most frequent cause of death in women up to about 1800 (after the hazards of pregnancy and childbirth) was burns from standing cooking at an open fire.
Research goes on constantly into the side effects of new technology. That something is being investigated doesn't necessarily mean that it will be proved to be unacceptable in use. What matters are the results of good research and the regulation of the manufacture and sales of the technology.
With energy prices rising exponentially, and alternative cooking and lighting methods like halogen ovens and light bulbs being used more and more, the public needs to know how to use them properly, and to read all that boring safety advice at the start of the manual.