Soft, highly deformable hard magnetic elastomers enable remote, untethered actuation for emerging applications in soft robotics and biomedicine, yet their reliable simulation remains demanding because large rotations and strains, near and full incompressibility, strong magneto mechanical coupling, and intermittent contact can occur simultaneously, often accompanied by numerical locking effects. We present a robust finite element formulation based on a geometrically exact two dimensional beam description enriched with an independent through thickness stretch, so that thickness changes are captured consistently alongside bending, shear, and axial deformation. A mixed incompressible hyperelastic setting is employed to represent near and pure incompressibility accurately while avoiding volumetric locking, and the discretization is designed to prevent shear locking in slender configurations. Magnetic actuation is introduced through an energy consistent model, and practical operation is addressed by incorporating unilateral interaction with rigid obstacles through a penalty based contact treatment complemented by Coulomb friction. Representative simulations demonstrate stable field controlled deformation and reliable contact behaviour across a range of slenderness ratios, highlighting an efficient and predictive computational route for multiphysics modelling of highly deformable magnetic structures, while extensions to soft magnetic materials are currently under consideration.