We show that a suspension of non-Brownian calcite particles in glycerol-water mixtures can be tuned continuously from being a yield-stress suspension to a shear-thickening suspension--without a measurable yield stress--by the addition of various surfactants. We interpret our results within a recent theoretical framework that models the rheological effects of stress-dependent constraints on inter-particle motion. Bare calcite particle suspensions are found to have finite yield stresses. In these suspensions, frictional contacts that constrain inter-particle sliding form at an infinitesimal applied stress and remain thereafter, while adhesive bonds that constrain inter-particle rotation are broken as the applied stress increases. Adding surfactants reduces the yield stress of such suspensions. We show that, contrary to the case of surfactant added to colloidal suspensions, this effect in non-Brownian suspensions is attributable to the emergence of a finite onset stress for the formation of frictional contacts. Our data suggest that the magnitude of this onset stress is set by the strength of surfactant adsorption to the particle surfaces, which therefore constitutes a new design principle for using surfactants to tune the rheology of formulations consisting of suspensions of adhesive non-Brownian particulates.