Large Language Models have demonstrated strong multilingual fluency, yet fluency alone does not guarantee socially appropriate language use. In high-context languages, communicative competence requires sensitivity to social hierarchy, relational roles, and interactional norms that are encoded directly in everyday language. Bangla exemplifies this challenge through its three-tiered pronominal system, kinship-based addressing, and culturally embedded social customs. We introduce BanglaSocialBench, the first benchmark designed to evaluate sociopragmatic competence in Bangla through context-dependent language use rather than factual recall. The benchmark spans three domains: Bangla Address Terms, Kinship Reasoning, and Social Customs, comprising 1,719 culturally grounded instances written and verified by native Bangla speakers. We evaluate twelve contemporary LLMs in a zero-shot setting and observe systematic patterns of cultural misalignment. Models frequently default to overly formal address forms, fail to recognize multiple socially acceptable address pronouns, and conflate kinship terminology across religious contexts. Our findings show that sociopragmatic failures are often structured and non-random; for example, inappropriate addressing choices concentrate heavily in downward-hierarchy (Elder→Younger) and informal contexts. This reveals persistent limitations in how current LLMs infer and apply culturally appropriate language use in realistic Bangladeshi social interactions.