As Large Language Models (LLMs) increasingly encourage users to disclose personal profiles for tailored assistance, measuring their political alignment becomes increasingly important. However, many existing benchmarks for assessing political behavior rely on closed-ended questions and do not fully capture how a model's stance may adapt to user-provided context during interaction. We introduce a framework that disentangles two distinct triggers of political sycophancy: opinion (aligning with explicit narratives) and identity (stereotyping based on demographic labels). Using 450 manually-checked political dilemmas as controlled probes, we evaluate 13 instruction-tuned LLMs. We uncover a dissociation: a model's susceptibility to explicit opinions does not necessarily predict its susceptibility to identity cues, and vice versa. When both signals are present, their effects are generally sub-additive rather than simply additive. Additionally, system-level personas primarily shift a model's baseline stance while having limited effect on the stance shift caused by user opinion or identity. Ultimately, our results suggest that LLM political stance is interactively and steerably vulnerable rather than being a fixed trait, highlighting how personalization may amplify identity- or opinion-conditioned shifts in the model's behaviors.

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