Standard evaluation practices assume that large language model (LLM) outputs are stable when prompts are embedded in contextually equivalent discourses. Here, we test this assumption in the setting of gender inference. Using a controlled pronoun selection task, we introduce minimal, theoretically uninformative discourse context and find that this induces large, systematic shifts in model outputs. Correlations with cultural gender stereotypes, present in decontextualized settings, weaken or disappear once context is introduced, while theoretically irrelevant features, such as the gender of a pronoun for an unrelated referent, become the most informative predictors of model behavior. A Contextuality-by-Default analysis reveals that, in 19--52\% of cases across models, this dependence persists after accounting for all marginal effects of context on individual outputs and cannot be attributed to simple pronoun repetition. These findings show that LLM outputs violate contextual invariance even under near-identical syntactic formulations, with implications for bias benchmarking and deployment in high-stakes settings.