Multimodal remote sensing image classification has attracted significant attention due to its capability to integrate complementary information from diverse data sources. However, most existing methods assume that co-registered multimodal observations share a single clean semantic ground-truth label and do not consider the controlled setting in which each modality is associated with an independently corrupted supervision stream derived from that shared label. Existing noisy-label learning methods are primarily designed for a single supervision stream and are therefore not directly applicable to this setting. To address this issue, this paper proposes a robust multimodal remote sensing image classification framework tailored for scenarios involving modality-specific noisy label. The core of the proposed method consists of a class-adaptive dynamic sample selection strategy and a confidence-aware robust training strategy. Specifically, Gaussian Mixture Models are employed to estimate sample confidence for each modality individually, with class-adaptive dynamic thresholds determined through class-distribution adaptive modeling. Based on the confidence scores and thresholds from both modalities, training samples are dynamically divided into three separate groups. Each group undergoes a different multimodal joint training strategy to mitigate the impact of noisy labels. Furthermore, we incorporate inter-modal prediction consistency constraint and cross-modal contrastive learning to enhance semantic alignment and feature discriminability of the multimodal fusion networks. Experiments conducted on three public multimodal remote sensing image datasets (Houston2013, Berlin, Augsburg) under various simulated modality-specific noisy label conditions. The results demonstrate that the proposed method consistently outperforms state-of-the-art approaches across different noise types and intensities, exhibiting superior robustness and generalization.The code is available at https://github.com/AAAA-CS/MNLL.