Recently, neighbor-based contrastive learning has been introduced to effectively exploit neighborhood information for clustering. However, these methods rely on the homophily assumption-that connected nodes share similar class labels and should therefore be close in feature space-which fails to account for the varying homophily levels in real-world graphs. As a result, applying contrastive learning to low-homophily graphs may lead to indistinguishable node representations due to unreliable neighborhood information, making it challenging to identify trustworthy neighborhoods with varying homophily levels in graph clustering. To tackle this, we introduce a novel neighborhood Neutral Contrastive Graph Clustering method, NeuCGC, that extends traditional contrastive learning by incorporating neutral pairs-node pairs treated as weighted positive pairs, rather than strictly positive or negative. These neutral pairs are dynamically adjusted based on the graph's homophily level, enabling a more flexible and robust learning process. Leveraging neutral pairs in contrastive learning, our method incorporates two key components: (1) an adaptive contrastive neighborhood distribution alignment that adjusts based on the homophily level of the given attribute graph, ensuring effective alignment of neighborhood distributions, and (2) a contrastive neighborhood node feature consistency learning mechanism that leverages reliable neighborhood information from high-confidence graphs to learn robust node representations, mitigating the adverse effects of varying homophily levels and effectively exploiting highly trustworthy neighborhood information. Experimental results demonstrate the effectiveness and robustness of our approach, outperforming other state-of-the-art graph clustering methods. Our code is available at https://github.com/THPengL/NeuCGC.