Offline reinforcement learning (RL) algorithms have shown promising results in domains where abundant pre-collected data is available. However, prior methods focus on solving individual problems from scratch with an offline dataset without considering how an offline RL agent can acquire multiple skills. We argue that a natural use case of offline RL is in settings where we can pool large amounts of data collected in various scenarios for solving different tasks, and utilize all of this data to learn behaviors for all the tasks more effectively rather than training each one in isolation. However, sharing data across all tasks in multi-task offline RL performs surprisingly poorly in practice. Thorough empirical analysis, we find that sharing data can actually exacerbate the distributional shift between the learned policy and the dataset, which in turn can lead to divergence of the learned policy and poor performance. To address this challenge, we develop a simple technique for data- sharing in multi-task offline RL that routes data based on the improvement over the task-specific data. We call this approach conservative data sharing (CDS), and it can be applied with multiple single-task offline RL methods. On a range of challenging multi-task locomotion, navigation, and vision-based robotic manipulation problems, CDS achieves the best or comparable performance compared to prior offline multi- task RL methods and previous data sharing approaches.