Socially Unacceptable Discourse (SUD) analysis is crucial for maintaining online positive environments. We investigate the effectiveness of Entailment-based zero-shot text classification (unsupervised method) for SUD detection and characterization by leveraging pre-trained transformer models and prompting techniques. The results demonstrate good generalization capabilities of these models to unseen data and highlight the promising nature of this approach for generating labeled datasets for the analysis and characterization of extremist narratives. The findings of this research contribute to the development of robust tools for studying SUD and promoting responsible communication online.