Large language models (LLMs) are increasingly used to answer questions about politically contentious issues, yet evaluations typically treat a model's stance as a relatively stable property. Real users, however, communicate political signals through their terminology, assumptions, and personal context. We investigate whether such signals produce ideological mimicry: systematic shifts in the political stance expressed by an LLM toward the position conveyed by the interaction. If LLMs adapt their responses to these signals, they risk creating personalised political information environments in which users with opposing views receive systematically different accounts of the same issue, potentially reinforcing existing divisions. We build the Poli-SHIFT dataset and evaluation framework and assess seven open-weight LLMs across ten contentious political topics in the United States, United Kingdom, and Australia, systematically manipulating contested terminology, politically valenced premises, and user information, and eliciting responses in both multiple-choice and open-text formats. Across models, we find robust evidence that prompt framing shapes the political stance of LLM outputs. Changing terminology alone reverses which side of an issue a model supports in 16.9% of matched comparisons. Stated political ideology also systematically shifts responses toward the user's position. These findings show that political stance is not a fixed property of LLMs; the views expressed are conditional on the interaction with the user. As LLMs become increasingly personalised sources of information, such interaction-dependent adaptation could contribute to political information environments that reinforce users' existing perspectives.

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