Multimodal sentiment analysis (MSA) has emerged as a prominent research frontier, enabling a comprehensive understanding of complex human emotions through the synergistic integration of heterogeneous multimodal signals. However, most existing approaches rely on idealized signal distribution assumptions, overlooking the detrimental impact of demographic bias on representation fairness and fusion robustness. This paper proposes a Label-Guided Contrastive Decoupling Fusion (LGCDF) framework that enhances model robustness to demographic bias by learning and fusing multimodal representations invariant to Sensitive Attributes (SAs). Specifically, the proposed LGCDF framework employs gender-sensitive attribute information as modality-level constraints to achieve language-centric cross-modal sentiment alignment, which is accomplished by computing contrastive losses between text–audio and text–visual feature pairs. Moreover, it introduces a SA-guided contrastive decoupling mechanism that decomposes multimodal representations into SA-related and -independent components. The SA-independent components are subsequently fused through a cross-modal attention fusion strategy, thereby facilitating fair sentiment representation and enabling efficient and robust multimodal information fusion. Extensive experimental results demonstrate that the proposed LGCDF framework achieves superior performance in fair representation learning and cross-modal information fusion while maintaining strong robustness under varying gender distribution biases.