We present the classical electromagnetic theory framework of reflection of a light beam carrying Orbital Angular Momentum (OAM) by an in-plane magnetic structure with generic symmetry. Depending on the magnetization symmetry, we find a change in the OAM content of the reflected beam due to magneto-optic interaction and an asymmetric far-field intensity profile. This leads to three types of Magnetic Helicoidal Dichroism (MHD), observed when switching the OAM of the incoming beam, the magnetization sign, or both. In cases of sufficient symmetries, we establish analytical formulas which link an experimentally accessible MHD signal up to 10% to the Magneto-Optical Kerr Effect (MOKE) constants. Magnetic vortices are particularly enlightening and promising targets, for which we explore the implications of our theory in the joint publication XX XXX XXXXXX.