The study of dark matter admixed neutron stars has the potential to advance our understanding of dark matter particle candidates. However, the large parameter space of dark matter particle masses restricts a systematic, model-independent study. In this analysis, we employ agnostic hadronic and dark-matter equations of state to construct dark-matter-admixed neutron stars within a two-fluid formalism. Dark matter is characterized solely by its low-density equation of state and mass and is modeled as a Fermi gas, while hadronic matter is anchored at low and high densities by chiral effective field theory and perturbative quantum chromodynamics calculations. A speed-of-sound parametrization describes the intermediate- and high-density regimes of both hadronic and dark matter, enabling an agnostic treatment of the dark matter equation of state that is constrained only by thermodynamic consistency and does not favor softer or stiffer behavior. Within this agnostic framework, we find that dark matter does not generically compactify the star: light dark matter forms extended halos that raise the tidal deformability, while heavy dark matter forms compact cores that lower it. Consequently, the dominant observational constraint shifts from gravitational-wave tidal deformability for light, halo-dominated models to NICER mass-radius data for heavy, core-dominated models. Using current data at $1\sigma$, we constrain the dark matter fraction to $f_{DM}\lesssim 0.11$ for light dark matter. By treating the medium- and high-density dark matter equation of state agnostically within a fermionic framework, our approach yields conservative and broadly applicable bounds on the dark matter content of neutron stars. Neutron stars with similar masses but very different tidal deformabilities could be a smoking-gun signature of dark matter in Neutron stars.