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Learning from Demonstration (LfD) is a powerful method for nonroboticists end-users to teach robots new tasks, enabling them to customize the robot behavior. However, modern LfD techniques do not explicitly synthesize safe robot behavior, which limits the deployability of these approaches in the real world. To enforce safety in LfD without relying on experts, we propose a new framework, ShiElding with Control barrier fUnctions in inverse REinforcement learning (SECURE), which learns a customized Control Barrier Function (CBF) from end-users that prevents robots from taking unsafe actions while imposing little interference with the task completion. We evaluate SECURE in three sets of experiments. First, we empirically validate SECURE learns a high-quality CBF from demonstrations and outperforms conventional LfD methods on simulated robotic and autonomous driving tasks with improvements on safety by up to 100%. Second, we demonstrate that roboticists can leverage SECURE to outperform conventional LfD approaches on a real-world knife-cutting, meal-preparation task by 12.5% in task completion while driving the number of safety violations to zero. Finally, we demonstrate in a user study that non-roboticists can use SECURE to efectively teach the robot safe policies that avoid collisions with the person and prevent cofee from spilling.