Side effects from targeted drugs is a serious concern. One reason is the nonselective binding of a drug to unintended proteins such as its paralogs, which are highly homologous in sequences and exhibit similar structures and drug-binding pockets. In this study, we analyzed amino acid residues with type-II functional divergence, i.e., sites that are conserved in sequence constraints but differ in physicochemical properties between paralogs, to identify targetable differences between two paralogs. We analyzed paralogous protein receptors in the glucagon-like subfamily, glucagon receptor (GCGR) and glucagon-like peptide-1 receptor (GLP-1R), which are clinically validated drug targets in patients with type 2 diabetes and exhibit divergence in ligands, showing opposing roles in regulating glucose homeostasis. We identified 8 residues related to type-II functional divergence, which are conserved in functional constraints but differ in physicochemical properties between GCGR and GLP-1R. We detected significant enrichment of predicted residues in binding sites of the antagonist MK-0893 to GCGR. We also identified a type-II functional divergence-related residue involved in ligand-specific effects that was critical for agonist-mediated activation of GLP-1R. We describe the important role of type-II functional divergence-related sites in paralog discrimination, enabling the identification of binding sites to reduce undesirable side effects and increase the target specificity of drugs.