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Hate speech is an important problem in the management of user-generated content. To remove offensive content or ban misbehaving users, content moderators need reliable hate speech detectors. Recently, deep neural networks based on the transformer architecture, such as the (multilingual) BERT model, achieve superior performance in many natural language classification tasks, including hate speech detection. So far, these methods have not been able to quantify their output in terms of reliability. We propose a Bayesian method using Monte Carlo dropout within the attention layers of the transformer models to provide well-calibrated reliability estimates. We evaluate and visualize the results of the proposed approach on hate speech detection problems in several languages. Additionally, we test if affective dimensions can enhance the information extracted by the BERT model in hate speech classification. Our experiments show that Monte Carlo dropout provides a viable mechanism for reliability estimation in transformer networks. Used within the BERT model, it ofers state-of-the-art classification performance and can detect less trusted predictions. Also, it was observed that affective dimensions extracted using sentic computing methods can provide insights toward interpretation of emotions involved in hate speech. Our approach not only improves the classification performance of the state-of-the-art multilingual BERT model but the computed reliability scores also significantly reduce the workload in an inspection of ofending cases and reannotation campaigns. The provided visualization helps to understand the borderline outcomes.