Moral values influence how we interpret and act upon the information we receive. Identifying human moral values is essential for artificially intelligent agents to co-exist with humans. Recent progress in natural language processing allows the identification of moral values in textual discourse. However, domain-specific moral rhetoric poses challenges for transferring knowledge from one domain to another.We provide the first extensive investigation on the effects of cross-domain classification of moral values from text. We compare a state-ofthe-art deep learning model (BERT) in seven domains and four cross-domain settings. We show that a value classifier can generalize and transfer knowledge to novel domains, but it can introduce catastrophic forgetting. We also highlight the typical classification errors in crossdomain value classification and compare the model predictions to the annotators agreement. Our results provide insights to computer and social scientists that seek to identify moral rhetoric specific to a domain of discourse.