One challenge that social media platforms are facing nowadays is hate speech. Hence, automatic hate speech detection has been increasingly researched in recent years - in particular with the rise of deep learning. A problem of these models is their vulnerability to undesirable bias in training data. We investigate the impact of political bias on hate speech classification by constructing three politically-biased data sets (left-wing, right-wing, politically neutral) and compare the performance of classifiers trained on them. We show that (1) political bias negatively impairs the performance of hate speech classifiers and (2) an explainable machine learning model can help to visualize such bias within the training data. The results show that political bias in training data has an impact on hate speech classification and can become a serious issue.