  Superconductivity and superfluidity with anisotropic pairing -- such as
$d$-wave in cuprates and $p$-wave in superfluid $^3$He -- are strongly
suppressed by impurities. Meanwhile, for applications, the robustness of Cooper
pairs to disorder is highly desired. Recently, it has been suggested that
unconventional systems become robust if the impurity scattering mixes
quasiparticle states only within individual subsystems obeying the Anderson
theorem that protects conventional superconductivity. Here, we experimentally
verify this conjecture by measuring the temperature dependence of the energy
gap in the polar phase of superfluid $^3$He. We show that oriented columnar
non-magnetic defects do not essentially modify the energy spectrum, which has a
Dirac nodal line. Although the scattering is strong, it preserves the momentum
along the length of the columns and forms robust subsystems according to the
conjecture. This finding may stimulate future experiments on the protection of
topological superconductivity against disorder and on the nature of topological
fermionic flat bands.
