Neutral and adaptive mutations are key players in the evolutionary dynamics of proteins at molecular, cellular and organismal levels. Conversely, largely destabilizing mutations are rarely tolerated by evolution, although their occurrence in diverse human populations has important roles in the pathogenesis of conformational diseases. We have recently proposed that divergence at certain sites from the consensus (amino acid) state during mammalian evolution may have rendered some human proteins more vulnerable towards disease-associated mutations, primarily by decreasing their conformational stability. We herein extend and refine this hypothesis discussing results from phylogenetic and structural analyses, structure-based energy calculations and structure-function studies at molecular and cellular levels. As proof-of-principle, we focus on different mammalian orthologues of the NQO1 (NAD(P)H:quinone oxidoreductase 1) and AGT (alanine:glyoxylate aminotransferase) proteins. We discuss the different loss-of-function pathogenic mechanisms associated with diseases involving the two enzymes, including enzyme inactivation, accelerated degradation, intracellular mistargeting, and aggregation. Last, we take into account the potentially higher robustness of mammalian orthologues containing certain consensus amino acids as suppressors of human disease, and their relation with different intracellular post-translational modifications and protein quality control capacities, to be discussed as sources of phenotypic variability between human and mammalian models of disease and as tools for improving current therapeutic approaches.