Gamma-ray bursts (GRBs) are the most luminous transients in the universe and are utilized as probes of early stars, gravitational wave counterparts and collisionless shock physics. 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 have yet been performed. Here we report the first coordinated simultaneous polarimetry in the optical and radio bands for the afterglow associated with 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 compared with the optical one. Our simultaneous polarization angle measurement and temporal polarization monitoring indicate the existence of cool electrons that increase the estimate of jet kinetic energy by a factor of more than 4 for this GRB afterglow. 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.