Social media platforms mediate professional communication, political expression, and community formation, making the rare instances when users collectively abandon an incumbent platform particularly consequential. Strong network effects raise switching costs and strengthen incumbents' positions, making coordinated exit difficult. Here we link 276,431 scholars on Twitter/X to their respective new profiles among the universe of all 16.7 million Bluesky accounts, tracked from January 2023 to December 2024, using a scalable, high-precision cross-platform matching pipeline. Exploiting exogenous variation from Brazil's court-ordered suspension of Twitter/X and a dynamic matching design, we show that adoption is peer-driven, treatment effects are short-lived and dose-dependent, and contagion is simple, not complex. Three patterns characterize adoption and retention. Adoption concentrates among users deeply embedded in Twitter's social graph. Public political expression predicts migration, consistent with homophilous inflows into a largely left-of-center Bluesky information space. Early reconnection with prior contacts predicts longer tenure and engagement. Our findings provide the first population-scale causal evidence of peer influence in a social media platform migration by exploiting exogenous exposure variation in a natural experiment and using daily dynamic matching. Rather than the complex contagion mechanism often emphasized in the literature, contagion is predominantly simple. Our findings recast migration as a multi-homing strategy that insures against governance uncertainty and show that users who quickly reconnect with prior contacts remain active longer on Bluesky.