Galactic cosmic rays (GCR) are among the main deterrents to manned space exploration. Currently, the most realistic way to reduce the dangers caused by GCR to acceptable levels is passive shielding. Light materials guarantee the strongest dose attenuation per unit mass. High-density polyethylene is considered the gold standard for radiation protection in space. Nevertheless, accelerator-based experimental campaigns already showed the advantages of more hydrogen-rich innovative shielding materials such as lithium hydride. The experimental campaigns of this work focused on the absorbed dose attenuation properties of lithium-based hydrides chemically stabilized with a paraffin matrix. Such materials were compared to pure lithium-based hydrides, polyethylene, structural materials such as spacecraft aluminum alloys and lithium batteries, and in situ shielding materials such as Moon regolith and its main components silicon and silicon dioxide. The experimental results were compared to simulations performed with PHITS, FLUKA, and Geant4, which are among the most used Monte Carlo codes for radiation protection in space. The simulations showed systematic differences and highlighted the pressing need for reliable nuclear cross-section models.