Globular protein sequences encode not only functional structures (the native state) but also protein foldability, i.e. a conformational search that is both efficient and robustly minimizes misfolding. Studies of mutations associated with toxic misfolding have yielded insights into molecular determinants of protein foldability. Of particular interest are residues that are conserved yet dispensable in the native state. Here, we exploited the mutant proinsulin syndrome (a major cause of permanent neonatal-onset diabetes mellitus) to investigate whether toxic misfolding poses an evolutionary constraint. Our experiments focused on an invariant aromatic motif (PheB24-PheB25-TyrB26) with complementary roles in native self-assembly and receptor binding. A novel class of mutations provided evidence that insulin can bind to the insulin receptor (IR) in two different modes, distinguished by a "register shift" in this motif, as visualized by molecular dynamics (MD) simulations. Register-shift variants are active but defective in cellular foldability and exquisitely susceptible to fibrillation in vitro Indeed, expression of the corresponding proinsulin variant induced endoplasmic reticulum stress, a general feature of the mutant proinsulin syndrome. Although not present among vertebrate insulin and insulin-like sequences, a prototypical variant ([GlyB24]insulin) was as potent as WT insulin in a rat model of diabetes. Although in MD simulations the shifted register of receptor engagement is compatible with the structure and allosteric reorganization of the IR-signaling complex, our results suggest that this binding mode is associated with toxic misfolding and so is disallowed in evolution. The implicit threat of proteotoxicity limits sequence variation among vertebrate insulins and insulin-like growth factors.