The interest in using reinforcement learning (RL) controllers in safety-critical applications such as robot navigation around pedestrians motivates the development of additional safety mechanisms. Running RL-enabled systems among uncertain dynamic agents may result in high counts of collisions and failures to reach the goal. The system could be safer if the pre-trained RL policy was uncertainty-informed. For that reason, we propose conformal predictive safety filters that: 1) predict the other agents' trajectories, 2) use statistical techniques to provide uncertainty intervals around these predictions, and 3) learn an additional safety filter that closely follows the RL controller but avoids the uncertainty intervals. We use conformal prediction to learn uncertainty-informed predictive safety filters, which make no assumptions about the agents' distribution. The framework is modular and outperforms the existing controllers in simulation. We demonstrate our approach with multiple experiments in a collision avoidance gym environment and show that our approach minimizes the number of collisions without making overly-conservative predictions.