Graph neural networks (GNNs) have achieved significant progress in graph-based learning tasks, yet their performance often deteriorates when facing heterophilous structures where connected nodes differ substantially in features and labels. To address this limitation, we propose GNNMoE, a novel entropy-driven mixture of message-passing experts framework that enables node-level adaptive representation learning. GNNMoE decomposes message passing into propagation and transformation operations and integrates them through multiple expert networks guided by a hybrid routing mechanism. And a routing entropy regularization dynamically adjusts soft weighting and soft top-$k$ routing, allowing GNNMoE to flexibly adapt to diverse neighborhood contexts. Extensive experiments on twelve benchmark datasets demonstrate that GNNMoE consistently outperforms SOTA node classification methods, while maintaining scalability and interpretability. This work provides a unified and principled approach for achieving fine-grained, personalized node representation learning.