Shipboard marine radar systems are essential for safe navigation, helping seafarers perceive their surroundings as they provide bearing and range estimations, object detection, and tracking. Since onboard systems have become increasingly digitized, interconnecting distributed electronics, radars have been integrated into modern bridge systems. But digitization increases the risk of cyberattacks, especially as vessels cannot be considered air-gapped. Consequently, in-depth security is crucial. However, particularly radar systems are not sufficiently protected against harmful network-level adversaries. Therefore, we ask: Can seafarers believe their eyes? In this paper, we identify possible attacks on radar communication and discuss how these threaten safe vessel operation in an attack taxonomy. Furthermore, we develop a holistic simulation environment with radar, complementary nautical sensors, and prototypically implemented cyberattacks from our taxonomy. Finally, leveraging this environment, we create a comprehensive dataset (RadarPWN) with radar network attacks that provides a foundation for future security research to secure marine radar communication.