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-of-the-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 cross-domain 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.