Video Anomaly Detection (VAD) remains a fundamental yet formidable task in the video understanding community, with promising applications in areas such as information forensics and public safety protection. Due to the rarity and diversity of anomalies, existing methods only use easily collected regular events to model the inherent normality of normal spatial-temporal patterns in an unsupervised manner. Previous studies have shown that existing unsupervised VAD models are incapable of label-independent data offsets (e.g., scene changes) in real-world scenarios and may fail to respond to light anomalies due to the overgeneralization of deep neural networks. Inspired by causality learning, we argue that there exist causal factors that can adequately generalize the prototypical patterns of regular events and present significant deviations when anomalous instances occur. In this regard, we propose Causal Representation Consistency Learning (CRCL) to implicitly mine potential scene-robust causal variable in unsupervised video normality learning. Specifically, building on the structural causal models, we propose scene-debiasing learning and causality-inspired normality learning to strip away entangled scene bias in deep representations and learn causal video normality, respectively. Extensive experiments on benchmarks validate the superiority of our method over conventional deep representation learning. Moreover, ablation studies and extension validation show that the CRCL can cope with label-independent biases in multi-scene settings and maintain stable performance with only limited training data available.