Large language models are increasingly used for Legal Judgment Prediction (LJP), raising concerns about demographic bias inherited from pre-training corpora and historical legal records. We investigate how fairness robustness changes under model adaptation in LJP through a controlled counterfactual evaluation across gender, ethnicity, and intersectional demographic groups. Using 23 demographic variants over encoder-based models and generative LLMs, we evaluate demographic sensitivity, counterfactual instability, and bias propagation under zero-shot, few-shot, and fine-tuned settings. Experiments show that model adaptation substantially affects fairness. Fine-tuning often improves predictive performance while simultaneously increasing demographic sensitivity and propagating biased supervision signals into downstream judicial predictions, whereas few-shot prompting generally produces smaller propagation effects. We further show that legal-domain specialization does not reliably guarantee fairness: legal-domain encoders span both highly robust and highly sensitive behavior after fine-tuning, and a legal-domain LLM is highly sensitive under few-shot prompting yet comparatively robust after fine-tuning under counterfactual perturbation.