I was always under the impression that microwave radiation, being non-ionizing, does not increase cancer-risk with exposure.
Other kind of radiation will resonate with bigger molecules and could do things like denaturalize them.
Have you ever fried an egg. You are denaturalizing a protein that is liquid and becomes solid, and you have done that just with heat alone.
You can actually denaturalize an egg in the microwave oven, and there are certainly lots of health problems when the microwave oven leaks microwaves.
When you denaturalize something in the body, it stops working as it should. This creates a cascade of things that stops working as they should.