Interaction of magnetic moment of point particles with external electromagnetic fields experiences unresolved theoretical and experimental discrepancies. In this work we point out several issues within relativistic quantum mechanics and QED and we describe effects related to a new covariant classical model of magnetic moment dynamics. Using this framework we explore the invariant acceleration experienced by neutral particles coupled to an external plane wave field through the magnetic moment: we study the case of ultrarelativistic Dirac neutrinos with magnetic moment in the range of 10−11 to 10−20μB; and we address the case of slowly moving neutrons. We explore how critical accelerations for neutrinos can be experimentally achieved in laser pulse interactions. The radiation of accelerated neutrinos can serve as an important test distinguishing between Majorana and Dirac nature of neutrinos.