Moving object segmentation (MOS) using a 3D light detection and ranging (LiDAR) sensor is crucial for scene understanding and identification of moving objects. Despite the availability of various types of 3D LiDAR sensors in the market, MOS research still predominantly focuses on 3D point clouds from mechanically spinning omnidirectional LiDAR sensors. Thus, we are, for example, lacking a dataset with MOS labels for point clouds from solid-state LiDAR sensors which have irregular scanning patterns. In this paper, we present a labeled dataset, called \textit{HeLiMOS}, that enables to test MOS approaches on four heterogeneous LiDAR sensors, including two solid-state LiDAR sensors. Furthermore, we introduce a novel automatic labeling method to substantially reduce the labeling effort required from human annotators. To this end, our framework exploits an instance-aware static map building approach and tracking-based false label filtering. Finally, we provide experimental results regarding the performance of commonly used state-of-the-art MOS approaches on HeLiMOS that suggest a new direction for a sensor-agnostic MOS, which generally works regardless of the type of LiDAR sensors used to capture 3D point clouds. Our dataset is available at https://sites.google.com/view/helimos.