Centromeric DNA and proteins evolve rapidly despite conserved function in mediating kinetochore-microtubule attachments during cell division. This paradox is explained by selfish DNA sequences preferentially binding centromeric proteins to disrupt attachments and bias their segregation into the egg (drive) during female meiosis. Adaptive centromeric protein evolution is predicted to prevent preferential binding to these sequences and suppress drive. Here, we test this prediction by defining the impact of adaptive evolution of the DNA-binding histone fold domain of CENP-T, a major link between centromeric DNA and microtubules. We reversed adaptive changes by creating chimeric variants of mouse CENP-T with the histone fold domain from closely related species, expressed exogenously in mouse oocytes or in a transgenic mouse model. We show that adaptive evolution of mouse CENP-T reduced centromere binding, which supports robust female gametogenesis. However, this innovation is independent of the centromeric DNA sequence, as shown by comparing the binding of divergent CENP-T variants to distinct centromere satellite arrays in mouse oocytes and in somatic cells from other species. Overall, our findings support a model in which selfish sequences drive to fixation, disrupting attachments of all centromeres to the spindle. DNA sequence-specific innovations are not needed to mitigate fitness costs in this model, so centromeric proteins adapt by modulating their binding to all centromeres in the aftermath of drive.