This paper presents a novel method for using Riemannian Motion Policies on volumetric maps, shown in the example of obstacle avoidance for Micro Aerial Vehicles (MAVs), Today, most robotic obstacle avoidance algorithms rely on sampling or optimization-based planners with volumetric maps. However, they are computationally expensive and often have inflexible monolithic architectures. Riemannian Motion Policies are a modular, parallelizable, and efficient navigation alternative but are challenging to use with the widely used voxel-based environment representations. We propose using GPU raycasting and tens of thousands of concurrent policies to provide direct obstacle avoidance using Riemannian Motion Policies in voxelized maps without needing map smoothing or pre-processing. Additionally, we present how the same method can directly plan on LiDAR scans without any intermediate map. We show how this reactive approach compares favorably to traditional planning methods and can evaluate up to 200 million rays per second. We demonstrate the planner successfully on a real MAV for static and dynamic obstacles. The presented planner is made available as an open-source package11https://github.com/ethz-asl/reactive_avoidance.