Microwaves are NOT ionizing radiation.
Good point! The dangers of microwave beams come mostly from two mechanisms:
a) Induced electrical currents - troublesome
per se in electronic circuits and other conducting objects where the 'stray' electricity can do bad things.
b) Induced heating - in less conductive materials... such as flesh, eyeballs, etc. Exactly what the consumer microwave oven is intended to do to food in a controlled space.
Some researchers also believe that recurring electromagnetic fields induced in tissue, nerves, etc. can alter normal biological mechanisms enough to cause cell abnormalities and possible disease. This is the common thread in most concerns about cellphone antennas radiating close to the body. No broad consensus exists yet in this regard, but frequent problems are not evident.