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High-risk materials predictions in fields such as nuclear reactor design, aerospace component qualification, and advanced energy storage systems demand not only accurate property forecasts but also uncertainty estimates that can be trusted under regulatory scrutiny. Materials graph neural networks have emerged as powerful tools for property prediction across composition and structure spaces, yet the overwhelming majority output a single scalar uncertainty that conflates two fundamentally different sources: epistemic uncertainty arising from incomplete or sparse training data and aleatoric uncertainty arising from irreducible noise in the underlying data-generation process itself. This conceptual framework paper demonstrates that failure to separate these uncertainty types leads to flawed risk assessments and inefficient decision-making. Epistemic uncertainty signals the need for additional data collection or targeted active learning, whereas aleatoric uncertainty signals the need for higher-fidelity data sources such as improved density-functional approximations or experimental validation. The proposed modular framework equips materials graph networks with dedicated estimators for each uncertainty type, an aggregator that applies risk-adjusted safety margins, a decision gate that triggers appropriate remediation actions, and a calibration certificate required for deployment in safety-critical contexts. Operational criteria are defined to validate the separation in practice, including data-scaling behavior, source-identification tests, and active-learning efficiency. By enabling precise mapping of uncertainty to actionable protocols, the framework bridges a critical gap between current uncertainty-quantification practices in graph neural networks and the stringent reliability requirements of high-risk materials engineering. It builds directly on foundational distinctions introduced for deep learning while adapting them to the unique challenges of crystal-graph representations and multi-fidelity materials data. The result is a conceptual blueprint that supports safer model deployment, more efficient discovery campaigns, and clearer pathways to regulatory approval.