Semi-supervised learning on real-world graphs is frequently challenged by heterophily, where the observed graph is unreliable or label-disassortative. Many existing graph neural networks either rely on a fixed adjacency structure or attempt to handle structural noise through regularization. In this work, we explicitly capture structural uncertainty by modeling a posterior distribution over signed adjacency matrices, allowing each edge to be positive, negative, or absent. We propose a sparse signed message passing network that is naturally robust to edge noise and heterophily, which can be interpreted from a Bayesian perspective. By combining (i) posterior marginalization over signed graph structures with (ii) sparse signed message aggregation, our approach offers a principled way to handle both edge noise and heterophily. Experimental results demonstrate that our method outperforms strong baseline models on heterophilic benchmarks under both synthetic and real-world structural noise.