I think defining what is damaging and what is not is the key. The World Health Organization has a good overview and defines each type of radiation. Below are all taken from the site and sums it up. So “yes” and “no” for the potential effects of RF on tissue. Is it ionizing or non-ionizing, but don't stand in front of a gigawatt antenna and think it will not harm you.
Ionizing radiation (harmful)
Ionizing radiation is radiation with enough energy so that during an interaction with an atom, it can remove tightly bound electrons from the orbit of an atom, causing the atom to become charged or ionized.
Here we are concerned with only one type of radiation, ionizing radiation, which occurs in two forms - waves or particles.
Forms of electromagnetic radiation. These differ only in frequency and wave length.
Heat waves
Radio waves
Infrared light
Visible light
Ultraviolet light
X rays
Gamma rays
Longer wave length, lower frequency waves (heat and radio) have less energy than shorter wave length, higher frequency waves (X and gamma rays). Not all electromagnetic (EM) radiation is ionizing. Only the high frequency portion of the electromagnetic spectrum which includes X rays and gamma rays is ionizing.
http://www.who.int/topics/radiation_non_ionizing/en/Non-ionizing (non harmful)
Non-ionizing radiation is the term given to radiation in the part of the electromagnetic spectrum where there is insufficient energy to cause ionization. It includes electric and magnetic fields, radio waves, microwaves, infrared, ultraviolet, and visible radiation.
http://www.who.int/ionizing_radiation/about/what_is_ir/en/