Plasma current filamentation of an ultrarelativistic electron beam impinging on an overdense plasma is investigated, with emphasis on radiation-induced electron polarization. Particle-in-cell simulations provide the classification and in-depth analysis of three different regimes of the current filaments, namely, the normal filament, abnormal filament, and quenching regimes. We show that electron radiative polarization emerges during the instability along the azimuthal direction in the momentum space, which significantly varies across the regimes. We put forward an intuitive Hamiltonian model to trace the origin of the electron polarization dynamics. In particular, we discern the role of nonlinear transverse motion of plasma filaments, which induces asymmetry in radiative spin flips, yielding an accumulation of electron polarization. Our results break the conventional perception that quasisymmetric fields are inefficient for generating radiative spin-polarized beams, suggesting the potential of electron polarization as a source of new information on laboratory and astrophysical plasma instabilities.