Soft robots are typically intended to operate in highly unpredictable and unstructured environments. Although their soft bodies help them to passively conform to their environment, the execution of specific tasks within such environments often requires the help of an operator that supervises the interaction between the robot and its environment and adjusts the actuation inputs in order to successfully execute the task. However, direct observation of the soft robot is often impeded by the environment in which it operates. Therefore, the operator has to depend on a real-time simulation of the soft robot based on the signals from proprioceptive sensors. However, the complicated three-dimensional (3D) configurations of the soft robot can be difficult to interpret using traditional visualization techniques. In this work, we present an open-source framework for real-time 3D reconstruction of soft robots in eXtended Reality (Augmented and Virtual Reality), based on signals from their proprioceptive sensors. This framework has a Robot Operating System (ROS) backbone, allowing for easy integration with existing soft robot control algorithms for intuitive and real-time teleoperation. This approach is demonstrated in Augmented Reality using a Microsoft Hololens device and runs at up to 60 FPS. We explore the influence that system parameters such as mesh density and armature complexity have on the reconstruction's key performance metrics (i.e., speed, scalability). The open-source framework is expected to function as a platform for future research and developments on real-time remote control of soft robots operating in environments that impede direct observation of the robot.