I learned from Wikipedia that neutrinos "are not affected by the electromagnetic forces". How was this identified experimentally?
Experimentally it has been found that neutrinos travel in a straight line through matter, unless they interact directly with nuclei on the way into a spate of particles. Their path is not affected by the magnetic field of a bubble chamber for example. (The OPERA neutrinos travel kilometers in a straight line unaffected by the magnetic field of the earth).
They leave no ionization trace in matter, as the other particles in the bubble chamber event.
Thus they are not charged.
They can interact electromagnetically with other charged particles through higher order Feynman diagrams, but as this would require a first weak vertex, the probability of interaction electromagnetically is very low and can be ignored to all practical purposes.
Neutrinos carry no electric charge and hence can't interact by electromagnetism.
I don't know if anyone has attempted to measure the charge on a neutrino, but you can tell immediately that they carry at most a very very small charge since they interact so weakly with matter. If they carried a significant charge they would be strongly scattered by matter just like all the other charged particles.