In dendritic solidification, growth morphologies often display a pronounced sensitivity to small changes in composition. To gain insight into the origins of this phenomenon, we undertake an atomistic calculation of the magnitude and anisotropy of the crystal-melt interfacial free energy in a model alloy system featuring no atomic size mismatch and relatively ideal solution thermodynamics. By comparing the results of these calculations with predictions from recent phase-field calculations, we demonstrate that alloying gives rise to changes in free-energy anisotropies that are substantial on the scale required to induce changes in growth orientations.