Automatic tissue segmentation of fetal brain images is essential for the quantitative analysis of prenatal neurodevelopment. However, producing voxel-level annotations of fetal brain imaging is time-consuming and expensive. To reduce labeling costs, we propose a practical unsupervised domain adaptation (UDA) setting that adapts the segmentation labels of high-quality fetal brain atlases to unlabeled fetal brain MRI data from another domain. To address the task, we propose a new UDA framework based on Appearance and Structure Consistency, named ASC. We adapt the segmentation model to the appearances of different domains by constraining the consistency before and after a frequency-based image transformation, which is to swap the appearance between brain MRI data and atlases. Consider that even in the same domain, the fetal brain images of different gestational ages could have significant variations in the anatomical structures. To make the model adapt to the structural variations in the target domain, we further encourage prediction consistency under different structural perturbations. Extensive experiments on FeTA 2021 benchmark demonstrate the effectiveness of our ASC in comparison to registration-based, semi-supervised learning-based, and existing UDA-based methods.