Intraoperative navigation in spine surgery demands millimeter-level accuracy. Currently, this is achieved through radiation-intensive intraoperative imaging and bone-anchored markers that are invasive and disrupt surgical workflow. Markerless RGB-D registration methods offer a promising alternative. However, existing approaches rely on weak segmentation labels to isolate relevant anatomical structures, potentially propagating errors through the registration process. We present End2Reg, an end-to-end deep learning framework that jointly optimizes segmentation and registration, eliminating the need for segmentation labels and manual steps. The network learns task-specific segmentation masks optimized for registration, guided solely by the registration objective without explicit segmentation supervision. End2Reg achieves state-of-the-art performance on ex- and in-vivo benchmarks, reducing median Target Registration Error by 32% and mean Root Mean Square Error by 61%, while maintaining robust performance under partial occlusions. Ablation results confirm that end-to-end optimization significantly improves registration accuracy. Overall, End2Reg advances towards fully automatic, markerless intraoperative navigation. Code and interactive visualizations are available at: https://lorenzopettinari.github.io/end-2-reg/.