People increasingly use large language models (LLMs) for everyday moral and interpersonal guidance, yet these systems cannot interrogate missing context and judge dilemmas as presented. We introduce a perturbation framework for testing the stability and manipulability of LLM moral judgments while holding the underlying moral conflict constant. Using 2,939 dilemmas from r/AmItheAsshole (January-March 2025), we generate three families of content perturbations: surface edits (lexical/structural noise), point-of-view shifts (voice and stance neutralization), and persuasion cues (self-positioning, social proof, pattern admissions, victim framing). We also vary the evaluation protocol (output ordering, instruction placement, and unstructured prompting). We evaluated all variants with four models (GPT-4.1, Claude 3.7 Sonnet, DeepSeek V3, Qwen2.5-72B) (N=129,156 judgments). Surface perturbations produce low flip rates (7.5%), largely within the self-consistency noise floor (4-13%), whereas point-of-view shifts induce substantially higher instability (24.3%). A large subset of dilemmas (37.9%) is robust to surface noise yet flips under perspective changes, indicating that models condition on narrative voice as a pragmatic cue. Instability concentrates in morally ambiguous cases; scenarios where no party is assigned blame are most susceptible. Persuasion perturbations yield systematic directional shifts. Protocol choices dominate all other factors: agreement between structured protocols is only 67.6% (kappa=0.55), and only 35.7% of model-scenario units match across all three protocols. These results show that LLM moral judgments are co-produced by narrative form and task scaffolding, raising reproducibility and equity concerns when outcomes depend on presentation skill rather than moral substance.