Person re-identification (Re-ID) across RGB and depth modalities offers complementary cues for robust pedestrian matching under challenging conditions. However, the significant discrepancy between RGB appearance features and depth structural features complicates cross-modal alignment. Existing methods either depend on static architectural designs or impose strong constraints to capture the common features of the two modalities, often suffering from branch imbalance or distorted identity features. In this work, we propose a novel framework, Dynamic Correlation-Guided Disentanglement and Contrastive Learning (DCG-DCL), for RGB-D cross-modal Re-ID. First, the Dynamic Correlation-guided Disentanglement (DCGD) dynamically decouples features with the guidance of inter-modal correlation, which explicitly enforces common-feature learning via a cross-correlation constraint and adaptively separates common and unique components without predefined assumptions. Second, a Common & Unique Contrastive Learning (CUCL) strategy fully leverages these decoupled features, which aligns RGB/depth features closer to their common representation and pushes them away from unique redundancies. This dual mechanism effectively narrows modality discrepancy and boosts robustness against modality-specific noise. Extensive experiments on multiple public benchmarks demonstrate that our method achieves state-of-the-art performance, with ablation studies validating the necessity of each component.