Whole-body teleoperation is essential for scalable robot data collection in loco-manipulation tasks, yet existing approaches relying on exoskeleton suits or multi-camera setups impose prohibitive cost, complexity, and environmental constraints. Recent methods using a single extended reality (XR) device with end-to-end reinforcement learning policies partially address these limitations but require robot-specific retraining, suffer from out-of-distribution failures, and rely on motion retargeting that neglects dynamic feasibility. We propose a hierarchical whole-body teleoperation framework driven by a single XR device that generalizes across diverse robot morphologies without retraining robot-specific policies. A Model Predictive Control (MPC)-based motion retargeter jointly optimizes alignment with the operator's intent and the robot's dynamic feasibility, generating optimal commands for existing low-level controllers. To ensure robust online execution, we introduce a state synchronization method that resets the simulator state at each MPC step to handle noisy real-world measurements and contact sensitivity, and integrate SLAM-based global pose feedback to mitigate long-term drift. Simulation results show higher success rates on whole-body control tasks for both a humanoid (over 30% lower completion time and 20% lower power consumption) and a mobile manipulator (zero collisions) compared to baselines. Real-world experiments further validate the effectiveness and flexibility of our method, demonstrating the successful deployment of the proposed retargeter on both platforms for whole-body control tasks and the ease of allowing users to adjust teleoperation behavior based on their preferences. This plug-and-play framework offers a scalable, morphology-agnostic solution for whole-body robot teleoperation, enabling real-time behavioral customization and broad applicability across platforms.