As long as I can remember, there have been periodic and generally low level concerns about non-ionizing radiation--the type of energy radio signals represent. By non-ionizing, we mean that the signals are not capable of dislodging electrons atoms or molecules, as are x-rays or gamma rays. Ionizing radiation, in high doses, is carcinogenic, though useful in low doses.
Non-ionizing radiation can cause tissue heating, as you can experience with food in a microwave oven. The health concerns about non-ionizing radiation come from the potential long term exposure. As with any form of natural radiation (sunlight, for example), the key is exposure levels.
The key thing about non-ionizing radiation is that it is found, in real-world communications cases, at very low power levels. Also, signals decay logarithmically.
This is an illustration of how a Wi-Fi router’s power levels drop rapidly with distance. Power levels drop more than half in the first two meters. Once people are about four meters from the router, signal levels have dropped from milliWatts to microWatts, about an order of magnitude (10 times).
Some people are concerned about power emitted from mobile cell towers. Keep in mind that mobile radios on cell towers have power levels that decay just as do Wi-Fi signals. Some liken the power levels of a mobile radio on a tower to that of a light bulb.
Radio signals weaken (attenuate) logarithmically, by powers of 10, so the power levels decay quite rapidly.
Basically, doubling the distance of a receiver from a transmitter means that the strength of the signal at that new location is 50 percent of its previous value. Just three meters from the antenna, a cell tower radio’s power density has dropped by an order of magnitude (10 times).
At 10 meters--perhaps to the base of the tower, power density is down two orders of magnitude. At 500 meters, a distance a human is using the signals, power density has dropped six orders of magnitude.
Though there is no scientific evidence that such low levels of non-ionizing radiation actually have health effects, such as causing cancer, a prudent human will limit the amount of exposure, just as one takes the prudent risk of wearing a seat belt in an automobile, minimizing time spent in the sun and so forth.