Learning-based scene representations such as neural radiance fields or light field networks, that rely on fitting a scene model to image observations, commonly encounter challenges in the presence of inconsistencies within the images caused by occlusions, inaccurately estimated camera parameters or effects like lens flare. To address this challenge, we introduce RANdom RAy Consensus (RANRAC), an efficient approach to eliminate the effect of inconsistent data, thereby taking inspiration from classical RANSAC based outlier detection for model fitting. In contrast to the down-weighting of the effect of outliers based on robust loss formulations, our approach reliably detects and excludes inconsistent perspectives, resulting in clean images without floating artifacts. For this purpose, we formulate a fuzzy adaption of the RANSAC paradigm, enabling its application to large scale models. We interpret the minimal number of samples to determine the model parameters as a tunable hyperparameter, investigate the generation of hypotheses with data-driven models, and analyse the validation of hypotheses in noisy environments. We demonstrate the compatibility and potential of our solution for both photo-realistic robust multi-view reconstruction from real-world images based on neural radiance fields and for single-shot reconstruction based on light-field networks. In particular, the results indicate significant improvements compared to state-of-the-art robust methods for novel-view synthesis on both synthetic and captured scenes with various inconsistencies including occlusions, noisy camera pose estimates, and unfocused perspectives. The results further indicate significant improvements for single-shot reconstruction from occluded images.