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The Stoner instability remains a cornerstone for understanding metallic ferromagnets. This instability captures the interplay of Coulomb repulsion, Pauli exclusion, and twofold fermionic spin degeneracy. In materials with spin–orbit coupling, this fermionic spin is generalized to a twofold degenerate pseudospin which is typically believed to have symmetry properties as spin. Here, we identify a distinct symmetry of this pseudospin that forbids it to couple to a Zeeman field. This “spinless” property is required to exist in five nonsymmorphic space groups and has nontrivial implications for superconductivity and magnetism. With Coulomb repulsion, Fermi surfaces composed primarily of this spinless pseudospin property give rise to Stoner instabilities into magnetic states that are qualitatively different than ferromagnets. These spinless-pseudospin ferromagnets break time-reversal symmetry, have a vanishing magnetization, are noncollinear, and exhibit momentum-dependent energy band spin-splittings. In superconductors, for all pairing symmetries and field orientations, this spinless pseudospin extinguishes paramagnetic limiting. We discuss applications to superconducting UCoGe and magnetic NiS_2-xSex