Constrained preference-conditioned MORL typically assumes full task observability, treating preferences and safety budgets as stationary task signals. In real-world deployment, however, these signals are often unreliable proxies: intent may drift, safety tolerances may shift with context, and exposed descriptors may be noisy, delayed, or incomplete. We therefore formulate constrained preference-conditioned MORL as a partially observed task-specification problem, where the agent must navigate a fundamental conflict between unreliable external signals and latent interaction dynamics. We propose \textbf{BECON}, a belief-conditioned framework for constrained MORL with drifting preferences and budgets, which infers latent task context from recent histories to estimate preferences and safety budgets. These estimates are fused with the exposed task signal via uncertainty-dependent gates, enabling the policy to defer to observations under high epistemic uncertainty while correcting them when history is informative. The fused context jointly conditions preference optimization and context-adaptive constraint enforcement. Experiments on diverse multi-objective control tasks demonstrate that BECON consistently improves over state-of-the-art MORL baselines, achieving stronger robustness and constraint satisfaction under task drift.

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