Whether an antiferromagnet can host direction-robust spin-polarized transport without a conventional spin-selective band gap remains a central challenge in antiferromagnetic spintronics. Here we establish a gapless, direction-robust spin-filtering mechanism in a compensated two-dimensional altermagnetic Weyl semimetal that requires neither a spin-selective band gap nor a large velocity contrast between spin projections. Using Janus monolayer Ta₂TeSeO as a realistic platform, we combine symmetry analysis with first-principles calculations, full-Brillouin-zone Wannier interpolation, and semiclassical transport. Rotating the Néel vector removes a unitary-mirror constraint and shifts one Weyl-cone pair away from its parent high-symmetry line. For an in-plane Néel vector, the residual C_2zT symmetry forbids the independent σ_y mass that would open a local gap, allowing the reconstructed cones to shift in momentum while remaining gapless. Breaking unitary C_2z simultaneously lifts the energy equivalence of the remaining mirror-pinned Weyl cones. The resulting coexistence of a metallic spin-projected manifold and a low-DOS Weyl-derived manifold produces a predominantly DOS-driven conductance imbalance. At charge neutrality and 20 K, the longitudinal conductivity polarization for n∥ x remains positive for every in-plane current direction and ranges from 76.4% to 82.0%. The degenerate in-plane magnetic anisotropy facilitates reversible switching between symmetry-related spin-filtering states using strain or weak anisotropic fields. This Néel-vector-driven symmetry mechanism provides a general route to direction-robust gapless spin filtering in compensated altermagnets.