Do language models adapt their linguistic style in an unbiased and socially appropriate way? We examine this issue in Japanese, a language with complex sociolinguistic constraints on stylistic adaptation between interlocutors, and we focus on the interplay between politeness and gendered linguistic styles. In terms of phenomena, we analyze morphologically encoded levels of formality alongside gender-indexical cues. In terms of methods, we analyze model behavior as well as human perceptions of generated outputs. Concretely, we first curate a novel set of 900 topic-balanced prompts with systematic formality and gendered-style variants. We then use these prompts to examine the behavior of four models, finding weak-to-moderate but consistent formality adaptation, with stronger adaptation to masculine-style than to feminine-style questions. Finally, we conduct a human perception study, showing that formality-mismatched responses are perceived as less appropriate than matched responses, with judgments strongly shaped by situational context. Taken together, our findings highlight the value of stylistic adaptation that is broadly invariant to gender-indexical cues and sensitive to situational context, with direct implications for conversational system design.