Context. Most massive protostars exhibit bipolar outflows. Nonetheless, there is no consensus regarding the mechanism at the origin of these outflows, nor on the cause of the less-frequently observed monopolar outflows. Aims. We aim to identify the origin of early massive protostellar outflows, focusing on the combined effects of radiative transfer and magnetic fields in a turbulent medium. Methods. We use four state-of-the-art radiation-magnetohydrodynamical simulations following the collapse of massive 100 M⊙ pre-stellar cores with the RAMSES code. Turbulence is taken into account via initial velocity dispersion. We use a hybrid radiative transfer method and include ambipolar diffusion. Results. Turbulence delays the launching of outflows, which appear to be mainly driven by magnetohydrodynamical processes. We study both the magnetic tower flow and the magneto-centrifugal acceleration as possible origins. Both contribute to the acceleration and the former operates on larger volumes than the latter. Our finest resolution, 5 AU, does not allow us to get converged results on magneto-centrifugally accelerated outflows. Radiative acceleration takes place as well, dominates in the star vicinity, enlarges the outflow extent, and has no negative impact on the launching of magnetic outflows (up to M ~17 M⊙, L ~ 105 L⊙). We observe mass outflow rates of 10−5−10−4 M⊙ yr−1 and momentum rates of the order ~10−4 M⊙ km s−1 yr−1. The associated opening angles (20−30deg when magnetic fields dominate) are in a range between observed values for wide-angle outflows and collimated outflows. If confirmed with a finer numerical resolution at the outflow interface, this suggests additional (de-)collimating effects. Outflows are launched nearly perpendicular to the disk and are misaligned with the initial core-scale magnetic fields, in agreement with several observational studies. In the most turbulent run, the outflow is monopolar. Conclusions. Magnetic processes are dominant over radiative ones in the acceleration of massive protostellar outflows of up to ~17 M⊙. Turbulence perturbs the outflow launching and is a possible explanation for monopolar outflows.