I'm no Darwinist, but EMF is non-ionizing because it lacks sufficient energy to move protons and neutrons around. It affects electrons only, and that effect is temporary with the net effect ultimately zero (an electron moved away from one atom is replaced immediately by one freed from an adjacent atom). That is electron drift, the basis of electric current. If nonionizing EMF could mutate DNA so readily, radio and TV engineers would be terribly mutated creatures begging to be killed to end their suffering, and the rest of us sitting in from of the high-voltage cathode-ray tubes of computer monitors would likely be not much better off.
I'm not addressing anything about the theory that this thread is based on, but EMF is the force used in particle accelerators(protons and neutrons).
I don't get what you're saying here because ionization has little or nothing to do with moving protons or neutrons around. It has everything to do with removing electrons, which you acknowledge can occur.
The statement that the net effect is zero and that a freed electron is immediately captured by an adjacent atom (which must also be an ion) is an oversimplification and not necessarily true.
Depending on conditions, electrons and ions can remain separated for considerably long periods of time in plasmas. However, the phrase 'long period' is a relative term and depends on the speed of other reactions or interactions of interest. Miliseconds are almost an eternity in plasma physics.