Gamma-ray bursts (GRBs) are the most luminous gamma-ray transients in the universe, and are utilized as probes of early stars, gravitational wave counterparts, and collision less shock physics. For understanding the fundamental physical quantities of GRB jets and their environments as well as their emission mechanism, coordinated multi-wavelength (semi-)simultaneous measurements are crucial as the global communities demonstrated in the past three decades. In spite of studies on polarimetry of GRBs in individual wavelengths that characterized intriguing properties of prompt emission and afterglow, no coordinated multi-wavelength measurements has yet been performed. Here, we report the first coordinated simultaneous polarimetry in the optical and radio bands for the afterglow associated to the typical long GRB 191221B. Our observations successfully caught the radio emission, which is not affected by synchrotron self-absorption, and show that the emission is depolarized in the radio band in comparison with the optical one. This result excludes a simple one-zone model that the polarization degree is nearly constant above the synchrotron self-absorption frequency, and has important implications for plasma-scale turbulent magnetic fields and existence of cool electrons. Our simultaneous polarization angle measurement supports the latter model rather than the former one. The existence of cool electrons increases the estimate of the total jet energy by a factor of > 2 for this typical GRB. Further coordinated multi-wavelength polarimetric campaigns would improve our understanding of the total jet energies and magnetic field configurations in the emission regions of various types of GRBs, which are required to comprehend the mass scales of their progenitor systems and the physics of collisionless shocks.