Relativistic thermal electrons moving in a large-scale magnetic field can produce synchrotron radiation. Linear synchrotron polarization can also be produced by the relativistic thermal electrons. In this paper, we utilize a hybrid thermal-nonthermal electron energy distribution to calculate circular synchrotron polarization. We further compute the radiative transfer of the synchrotron polarization in the optical and radio bands when we consider the contribution of the thermal electrons. We attempt to apply the polarization results to some astrophysical objects, such as kilonova like AT 2017gfo/GW170817, the fast radio burst (FRB), the gamma-ray burst afterglow, and the supernova remnant. The large optical depth of radiative transfer affects the small polarization degrees of these populations when the media surrounding the synchrotron sources take heavy absorption to the polarized photons. We need a strong magnetic field in our model to reproduce the linear and circular polarization properties that were observed in FRB 140514. This indicates that FRBs have a neutron star origin.