In this paper, we investigate the generalization capabilities of deep learning models to different target groups of hate speech under clean experimental settings. Furthermore, we assess the efficacy of three different strategies of unsupervised domain adaptation to improve these capabilities. Given the diversity of hate and its rapid dynamics in the online world (e.g. the evolution of new target groups like virologists during the COVID-19 pandemic), robustly detecting hate aimed at newly identified target groups is a highly relevant research question. We show that naively trained models suffer from a target group specific bias, which can be reduced via domain adaptation. We were able to achieve a relative improvement of the F1-score between 5.8% and 10.7% for out-of-domain target groups of hate speech compared to baseline approaches by utilizing domain adaptation.