We analyze publicly available US Supreme Court documents using automated stance detection. In the first phase of our work, we investigate the extent to which the Court's public-facing language is political. We propose and calculate two distinct ideology metrics of SCOTUS justices using oral argument transcripts. We then compare these language-based metrics to existing social scientific measures of the ideology of the Supreme Court and the public. Through this cross-disciplinary analysis, we find that justices who are more responsive to public opinion tend to express their ideology during oral arguments. This observation provides a new kind of evidence in favor of the attitudinal change hypothesis of Supreme Court justice behavior. As a natural extension of this political stance detection, we propose the more specialized task of legal stance detection with our new dataset SC-stance, which matches written opinions to legal questions. We find competitive performance on this dataset using language adapters trained on legal documents.