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Multi-property graph neural networks (GNNs) have emerged as the dominant paradigm in computational materials science, enabling a single equivariant backbone to simultaneously predict energies, forces, stresses, elastic tensors, band gaps, and other key properties from atomic structures. Proponents emphasize gains in data efficiency, regularization, and inductive bias transfer across tasks. However, this work reveals a fundamental and previously underappreciated limitation: equivariant error cancellation within shared representations. By enforcing rotational, translational, and permutation symmetries, equivariant GNN backbones map atomic structures into a constrained feature space where different physical properties transform under distinct irreducible representations. We demonstrate theoretically and conceptually that gradients arising from weakly correlated or anti-correlated properties frequently conflict within these shared layers. Such conflicts drive error cancellation—reductions in the aggregate multi-task loss that mask stagnant or deteriorating accuracy on individual targets—particularly when properties map to incompatible tensorial characters (scalars, vectors, rank-2 and higher tensors). We identify three regimes of representation sharing: beneficial (strongly aligned gradients), neutral (orthogonal gradients), and harmful (opposing gradients leading to representational compromise). Proof sketches show that equivariance tightens the feasible representation space and bounds gradient alignment more severely than in invariant architectures, systematically increasing the risk of harmful cancellation. Detection diagnostics and architectural mitigation strategies are proposed to identify and alleviate these effects. This analysis reframes the design of multi-property materials GNNs, demonstrating that joint training is not universally beneficial and can actively degrade specialization. It provides a principled foundation for next-generation architectures that preserve data efficiency while safeguarding per-property accuracy, advancing reliable data-driven materials discovery and design.