History illustrates that economic crises and other sociopolitical threats often lead to a rise of polarization and radicalism, whereby people become more susceptible to intolerant political messages, including propaganda and ideological rhetoric. Political science, sociology, economics, and psychology have explored many dimensions of this phenomenon, yet a critical piece of the puzzle is still missing: what cognitive and neural mechanisms in the brain mediate between these threats and responsiveness to political messages? To answer this question, here, we present a theory that combines cognitive neuroscience theories, namely stress-induced memory shift and competitive cognitive processes, with political science. Our Threat-based Neural Switch Theory posits that the processing of political information, similarly to other information processing, is shaped by the competitive interaction between goal-directed and habitual processes. Threats, including resource overload or scarcity, can shift neural networks toward receptiveness to oversimplified political messages. This theory sets out a research program aimed at discovering the cognitive and neural underpinning of how situational factors alter brain functions and modify political information processing.