Context. Frequency-dependent and hybrid approaches for the treatment of stellar irradiation are of primary importance in numerical simulations of massive star formation.Aims. We seek to compare outflow and accretion mechanisms in star formation simulations. We investigate the accuracy of a hybrid radiative transfer method using the gray M1 closure relation for proto-stellar irradiation and gray flux-limited diffusion (FLD) for photons emitted everywhere else.Methods. We have coupled the FLD module of the adaptive-mesh refinement code RAMSES with RAMSES-RT, which is based on the M1 closure relation and the reduced speed-of-light-approximation. Our hybrid (M1+FLD) method takes an average opacity at the stellar temperature for the M1 module, instead of the local environmental radiation field. Due to their construction, the opacities are consistent with the photon origin. We have tested this approach in radiative transfer tests of disks irradiated by a star for three levels of optical thickness and compared the temperature structure with the radiative transfer codes RADMC-3D and MCFOST. We applied it to a radiation-hydrodynamical simulation of massive star formation.Results. Our tests validate our hybrid approach for determining the temperature structure of an irradiated disk in the optically-thin (2% maximal error) and moderately optically-thick (error smaller than 25%) regimes. The most optically-thick test shows the limitation of our hybrid approach with a maximal error of 65% in the disk mid-plane against 94% with the FLD method. The optically-thick setups highlight the ability of the hybrid method to partially capture the self-shielding in the disk while the FLD alone cannot. The radiative acceleration is ≈100 times greater with the hybrid method than with the FLD. The hybrid method consistently leads to about + 50% more extended and wider-angle radiative outflows in the massive star formation simulation. We obtain a 17.6 M⊙ star at t ≃ 0.7τff, while the accretion phase is still ongoing, with a mean accretion rate of ≃7 × 10−4 M⊙ yr−1. Finally, despite the use of refinement to resolve the radiative cavities, no Rayleigh–Taylor instability appears in our simulations, and we justify their absence by physical arguments based on the entropy gradient.