Political moderation, a key attractor in democratic systems, proves highly fragile under realistic information conditions. We develop a stochastic model of opinion dynamics to analyze how noise and differential susceptibility reshape the political spectrum. Extending Marvel et al.'s deterministic framework, we incorporate stochastic media influence $zeta(t)$ and neuropolitically-grounded sensitivity differences ($sigma_y > sigma_x$). Analysis reveals the moderate population---stable in deterministic models---undergoes catastrophic collapse under stochastic forcing. This occurs through an effective deradicalization asymmetry ($u_{B}^{text{eff}} = u + sigma_y^2/2 > u_{A}^{text{eff}}$) that drives conservatives to extinction, eliminating cross-cutting interactions that sustain moderates. The system exhibits a phase transition from multi-stable coexistence to liberal dominance, demonstrating how information flow architecture---independent of content---systematically dismantles the political center. Our findings reveal moderation as an emergent property highly vulnerable to stochastic perturbations in complex social systems.