Humans adjust their style to suit the audience they are addressing. However, the extent to which LLMs adapt to different social contexts is largely unknown. As these models increasingly mediate human-to-human communication, their failure to adapt to diverse styles can perpetuate stereotypes and marginalize communities whose linguistic norms are less closely mirrored by the models, thereby reinforcing social stratification. We study the extent to which LLMs integrate into social media communication across different socioeconomic status (SES) communities. We collect a novel dataset from Reddit and YouTube stratified by SES. We prompt four LLMs with incomplete text from that corpus and compare the LLM-generated completions to the originals along 94 sociolinguistic metrics, including syntactic, rhetorical, and lexical features. LLMs modulate their style to lower and upper SES communities to only a minor extent, often resulting in approximation or caricature, and tend to emulate the style of upper SES more effectively. By better reflecting the linguistic norms of one group over the other, our findings (1) show how LLMs risk amplifying linguistic hierarchies and (2) call into question their validity for agent-based social simulation, survey experiments, and research relying on language style as a social signal.