Subgap states in semiconducting-superconducting nanowire hybrid devices are controversially discussed as potential topologically nontrivial quantum states. One source of ambiguity is the lack of an energetically and spatially well defined tunnel spectrometer. Here, we use quantum dots directly integrated into the nanowire during the growth process to perform tunnel spectroscopy of discrete subgap states in a long nanowire segment. In addition to subgap states with a standard magnetic field dependence, we find topologically trivial subgap states that are independent of the external magnetic field, i.e., that are pinned to a constant energy as a function of field. We explain this effect qualitatively and quantitatively by taking into account the strong spin-orbit interaction in the nanowire, which can lead to a decoupling of Andreev bound states from the field due to a spatial spin texture of the confined eigenstates. This result constitutes an important step forward in the research on superconducting subgap states in nanowires, such as Majorana bound states.