Using subparsec-scale-resolution radiation+hydrodynamical adaptive mesh refinement simulations deployed with the RAMSES code, we study the dynamics of supermassive black hole (SMBH) binaries embedded in gaseous nuclear circumbinary disks, where we investigate the effects of active galactic nucleus feedback on the SMBH binaries' migration behavior and disk structure. The radiative feedback effects are modeled by injecting photons that interact with the gas, through the adoption of a grid of BH emission spectra. We run simulations with initial conditions that lead by pure gravity plus hydrodynamics both to the formation of a low-density tidal cavity and to systems where gas–viscous diffusion is efficient enough to maintain a sizable gas reservoir surrounding the binary. For gap-forming binaries we find that orbital evolution is unchanged with the inclusion of feedback, but ionizing radiation photoevaporates gas that is at the outer edge of the low-density region. For non-gap-forming systems we find that when feedback is included a strong initial disruption of the circumbinary disk is followed by an eventual stabilization of the medium that can usher a return to a fast binary migration regime. All of this is possible as a result of how our simulations capture the ionization states of the nuclear disk region and how this affects the coupling efficiency decrease with respect to the radiative feedback.