As large language models (LLMs) are increasingly deployed in dialogue systems and interactive agents, their social adaptation during natural interaction has drawn growing attention. While prior work shows strong social regulation under explicit role or style instructions, it remains unclear whether LLMs can spontaneously perceive and respond to implicit social differences without explicit prompts. Focusing on high-context Chinese interactions, we identify a robust phenomenon termed Social Agnosia, where LLMs fail to adequately perceive and accommodate implicit social power, affective arousal, and epistemic status during natural interaction. To diagnose this behavior, we propose C-ISA, a framework grounded in Communication Accommodation Theory that decomposes social adaptation into three approximately orthogonal dimensions, and conduct controlled comparisons across multiple Chinese LLMs under implicit and explicit conditions. Results show that while models substantially adjust linguistic strategies under explicit conditioning, they exhibit socially insensitive and homogenized responses in natural interaction, revealing a structural gap between spontaneous behavior and conditioned capability. The C-ISA dataset is publicly available at https://github.com/ty373/C-ISA.