Paralogous genes are often functionally redundant for long periods of time. While their functions are preserved, paralogs accumulate cryptic changes in sequence and expression, which could modulate the impact of future mutations through epistasis. We examine the impact of mutations on redundant myosin proteins that have maintained the same binding preference despite having accumulated differences in expression levels and amino acid substitutions in the last 100 million years. By quantifying the impact of all single-amino acid substitutions in their SH3 domains on the physical interaction with their interaction partners, we show that the same mutations in the paralogous SH3s change binding in a paralog-specific and interaction partner-specific manner. This contingency is explained by the difference in promoter strength of the two paralogous myosin genes and epistatic interactions between the mutations introduced and cryptic divergent sites within the SH3s. One significant consequence of this contingency is that while some mutations would be sufficient to nonfunctionalize one paralog, they would have minimal impact on the other. Our results reveal how cryptic divergence, which accumulates while maintaining functional redundancy in cellular networks, could bias gene duplicates to specific fates.