Segmentation of fetal brain tissue from magnetic resonance imaging (MRI) plays a crucial role in the study of in utero neurodevelopment. However, automated tools face substantial domain shift challenges as they must be robust to highly heterogeneous clinical data, often limited in numbers and lacking annotations. Indeed, high variability of the fetal brain morphology, MRI acquisition parameters, and superresolution reconstruction (SR) algorithms adversely affect the model's performance when evaluated out-of-domain. In this work, we introduce FetalSynthSeg, a domain randomization method to segment fetal brain MRI, inspired by SynthSeg. Our results show that models trained solely on synthetic data outperform models trained on real data in out-ofdomain settings, validated on a 120-subject cross-domain dataset. Furthermore, we extend our evaluation to 40 subjects acquired using lowfield (0.55T) MRI and reconstructed with novel SR models, showcasing robustness across different magnetic field strengths and SR algorithms. Leveraging a generative synthetic approach, we tackle the domain shift problem in fetal brain MRI and offer compelling prospects for applications in fields with limited and highly heterogeneous data.