Interfaces are ubiquitous in materials science, and in devices in particular. As device dimensions are constantly shrinking, understanding the physical properties emerging at interfaces is crucial to exploit them for applications, here for spintronics. Using first-principles techniques and Monte Carlo simulations, we investigate the mutual magnetic interaction at the interface between graphene and an antiferromagnetic semiconductor BaMnO3. We find that graphene deeply affects the magnetic state of the substrate, down to several layers below the interface, by inducing an overall magnetic softening, and switching the in-plane magnetic ordering from antiferromagnetic to ferromagnetic. The graphene-BaMnO3 system presents a Rashba gap 300 times larger than in pristine graphene, leading to a flavor of quantum anomalous Hall effect (QAHE), a hybrid QAHE, characterized by the coexistence of metallic and topological insulating states. These findings could be exploited to fabricate devices that use graphene to control the magnetic configuration of a substrate.