A transition from solid-like to liquid-like behavior occurs when colloidal gels are subjected to a prolonged exposure to a steady shear. This phenomenon, which is characterized by a yielding point, is found to be strongly dependent on the packing fraction. However, it is not yet known how the effective inter-particle potential affects this transition. To this aim, we present a numerical investigation of the rheology of equilibrium gels in which a short-range depletion is complemented by a long-range electrostatic interaction. We observe a single yielding event in the stress-strain curve, occurring at a fixed strain. The stress overshoot is found to follow a power-law dependence on the Péclet number, with an exponent larger than that found in depletion gels, suggesting that its value may depend systematically on the underlying colloid-colloid interactions. We also establish a mapping between equilibrium states and steady states under shear, which allows us to identify the structural modifications induced by the presence of the shear. Remarkably, we find that steady states corresponding to the same Péclet number, obtained by different combinations of shear rate and solvent viscosity, show identical structural and rheological properties. Our results highlight the importance of understanding the coupling between colloidal interactions, solvent effects, and flow to be able to describe the microscopic organization of colloidal particles under shear.