We investigate resource allocation in integrated sensing and communication (ISAC) systems exploiting movable antennas (MAs) to enhance system performance. Unlike the existing ISAC literature, we account for dynamic radar cross-section (RCS) variations. Chance constraints are introduced and integrated into the sensing quality of service (QoS) framework to precisely control the impact of the resulting RCS uncertainties. Taking into account the dynamic nature of the RCS, we jointly optimize the MA positions and the communication and sensing beam design for minimization of the total transmit power at the base station (BS) while ensuring the individual communication and sensing task QoS requirements. To tackle the resulting non-convex mixed integer non-linear program (MINLP), we develop an iterative algorithm to obtain a high quality suboptimal solution. Our numerical results reveal that the proposed MA-enhanced ISAC system cannot only significantly reduce the BS transmit power compared to systems relying on fixed antenna positions and antenna selection but also demonstrates remarkable robustness to RCS fluctuations, underscoring the multifaceted benefits of exploiting MAs in ISAC systems.