Self-supervised learning (SSL) conventionally relies on the instance consistency paradigm, assuming that different views of the same image can be treated as positive pairs. However, this assumption breaks down for non-iconic data, where different views may contain distinct objects or semantic information. In this paper, we investigate the effectiveness of SSL when instance consistency is not guaranteed. Through extensive ablation studies, we demonstrate that SSL can still learn meaningful representations even when positive pairs lack strict instance consistency. Furthermore, our analysis further reveals that increasing view diversity, by enforcing zero overlapping or using smaller crop scales, can enhance downstream performance on classification and dense prediction tasks. However, excessive diversity is found to reduce effectiveness, suggesting an optimal range for view diversity. To quantify this, we adopt the Earth Mover's Distance (EMD) as an estimator to measure mutual information between views, finding that moderate EMD values correlate with improved SSL learning, providing insights for future SSL framework design. We validate our findings across a range of settings, highlighting their robustness and applicability on diverse data sources.