The integration of Large Language Models (LLMs) and Graph Neural Networks (GNNs) promises to unify semantic understanding with structural reasoning, yet existing methods typically rely on static, unidirectional pipelines. These approaches suffer from fundamental limitations: (1) Bidirectional Error Propagation, where semantic hallucinations in LLMs or structural noise in GNNs permanently poison the downstream modality without opportunity for recourse; (2) Semantic-Structural Dissonance, particularly in heterophilous settings where textual similarity contradicts topological reality; (3) a Blind Leading the Blind phenomenon, where indiscriminate alignment forces models to mirror each other's mistakes regardless of uncertainty. To address these challenges, we propose CO-EVOLVE, a dual-view co-evolution framework that treats graph topology and semantic embeddings as dynamic, mutually reinforcing latent variables. By employing a Gauss-Seidel alternating optimization strategy, our framework establishes a cyclic feedback loop: the GNN injects structural context as Soft Prompts to guide the LLM, while the LLM constructs favorable Dynamic Semantic Graphs to rewire the GNN. We introduce three key innovations to stabilize this evolution: (1) a Hard-Structure Conflict-Aware Contrastive Loss that warps the semantic manifold to respect high-order topological boundaries; (2) an Adaptive Node Gating Mechanism that dynamically fuses static and learnable structures to recover missing links; (3) an Uncertainty-Gated Consistency strategy that enables meta-cognitive alignment, ensuring models only learn from the confident view. Finally, an Entropy-Aware Adaptive Fusion integrates predictions during inference. Extensive experiments on public benchmarks demonstrate that CO-EVOLVE significantly outperforms state-of-the-art baselines, achieving average improvements of 9.07% in Accuracy and 7.19% in F1-score.