The stability of steady slip and homogeneous shear is studied for rate-hardening materials undergoing chemical reactions that produce weaker materials (reaction-weakening process), in drained conditions. In a spring- slider configuration, a linear perturbation analysis provides analytical expressions of the critical stiffness below which unstable slip occurs. In the framework of a frictional constitutive law, numerical tests are performed to study the effects of a nonlinear reaction kinetics on the evolution of the instability. Slip instabilities can be stopped at relatively small slip rates (only a few orders of magnitude higher than the forcing velocity) when the reactant is fully depleted. The stability analysis of homogeneous shear provides an independent estimate of the thickness of the shear localization zone due to the reaction weakening, which can be as low as 0.1 m in the case of lizardite dehydration. The potential effect of thermo-chemical pore fluid pressurization during dehydration is discussed, and shown to be negligible compared to the reaction-weakening effect. We finally argue that the slip instabilities originating from the reaction-weakening process could be a plausible candidate for intermediate depth earthquakes in subduction zones.