Safe clinical deployment of Large Language Models (LLMs) requires not only high accuracy but also robust uncertainty calibration to ensure models defer to clinicians when appropriate. Our paper investigates how social descriptors of a patient (specifically sexual orientation and religious affiliation) distort these uncertainty signals and model accuracy. Evaluating nine general-purpose and biomedical LLMs on 2,364 medical questions and their counterfactual variants, we demonstrate that identity markers cause a "calibration crisis". "Homosexual" markers consistently trigger performance drops, and intersectional identities produce idiosyncratic, non-additive harms to calibration. Moreover, a clinician-validated case study in an open-ended generation setting confirms that these failures are not an artifact of the multiple-choice format. Our results demonstrate that the presence of social identity cues does not merely shift predictions; it affects the reliability of confidence signals, posing a significant risk to equitable care and safe deployment in confidence-based clinical workflows.