Human space exploration requires low-mass textiles with high mechanical strength, thermal stability, durability, and protection against extreme environmental conditions. This critical narrative review evaluates the potential of plant biodiversity as a source of fibers, biomaterials, and bioinspired structures for sustainable space textile materials based on scientific literature retrieved from Scopus and Web of Science, complemented by technical information from the NASA Technical Reports Server. The reported maximum tensile strengths of individual flax, hemp, ramie, bamboo, and banana fibers reach 1830, 1110, 938, 800, and 914 MPa, respectively. However, these literature maxima should not be interpreted as allowable for aerospace design because plant-fiber properties exhibit substantial variability and require statistically based validation at the textile and component levels. Beyond structural applications, natural cellulosic and lignocellulosic fibers may also offer advantages for textile physiological functions, including moisture management and skin-contact comfort, although these attributes require validation under space-specific conditions. Nanocellulose and porous cellulosic materials show potential for insulation, membranes, and coatings, with thermal conductivities of ≤20 mW·m⁻¹·K⁻¹. Amazonian species, such as Attalea speciosa, Mauritia flexuosa, Manicaria saccifera, Euterpe oleracea, and Copernicia prunifera, exhibit promising properties for bio-based applications. However, moisture, radiation, abrasion, structural variability, thermal stability, and extraterrestrial dust remain key limitations, with no evidence of plant-derived fibers in operational EVA spacesuits. Surface modification can tailor wettability, interfacial compatibility, and stability. Their near-term use may focus on secondary and multifunctional components, whereas their long-term sustainability depends on modularity, repairability, material recovery, and in-space manufacturing. This perspective distinguishes the potential of EVA systems from their established use in IVA crew clothing.