Recent advances on 6D object pose estimation have achieved high performance on representative benchmarks such as LM-O, YCB-V, and T-Less. However, these datasets were captured under fixed illumination and camera settings, leaving the impact of real-world variations in illumination, exposure, gain or depth-sensor mode largely unexplored. To bridge this gap, we introduce SenseShift6D, the first RGB-D dataset that physically sweeps 13 RGB exposures, 9 RGB gains, auto-exposure, 4 depth-capture modes, and 5 illumination levels. For six common household objects, we acquire 198.8k RGB and 20.0k depth images (i.e., 795.4k RGB-D scenes), providing 1,380 unique sensor-lighting permutations per object pose. Experiments with state-of-the-art pretrained, generalizable pose estimators reveal substantial performance variation across lighting and sensor settings, despite their large-scale pretraining. Strikingly, even instance-level estimators-trained and tested on identical objects and backgrounds-exhibit pronounced sensitivity to environmental and sensor shifts. These findings establish sensor- and environment-aware robustness as an underexplored yet essential dimension for real-world deployment, and motivate SenseShift6D as a necessary benchmark for the community. Finally, to illustrate the opportunity enabled by this benchmark, we evaluate test-time multimodal sensor selection without retraining. An idealized (oracle) controller yields remarkable gains of up to +16.7 pp for generalizable models, whereas a practical consistency-based proxy improves performance only marginally, highlighting substantial headroom and the need for future research on reliable sensor-aware adaptation.