Fuzzy objects composed of hair, fur, or feather are impossible to scan even with the latest active or passive 3D scanners. We present a novel and practical neural rendering (NR) technique called neural opacity point cloud (NOPC) to allow high quality rendering of such fuzzy objects at any viewpoint. NOPC employs a learning-based scheme to extract geometric and appearance features on 3D point clouds including their opacity. It then maps the 3D features onto virtual viewpoints where a new U-Net based NR manages to handle noisy and incomplete geometry while maintaining translation equivariance. Comprehensive experiments on existing and new datasets show our NOPC can produce photorealistic rendering on inputs from multi-view setups such as a turntable system for hair and furry toy captures.