There is a theoretical way they could cause problems, though, which needs more investigation. DNA can conduct. It may be possible for DNA molecules to act as antennas and have a current induced in them from electromagnetic waves passing through.

Some researches believe that part of the mechanism used to detect and repair damage to our DNA involves sending a current through the DNA and looking for anomalies. Externally induced currents could interfere with that damage detection and repair.

There are some pretty amazing and subtle things going on in our cells.