  In hydrodynamics, for generic relaxations, the stress tensor and $U(1)$
charge current two-point functions are not time-reversal covariant. This
remains true even if the Martin-Kadanoff procedure happens to yield Onsager
reciprocal correlators. We consider linearised relativistic hydrodynamics on
Minkowski space in the presence of energy, $U(1)$ charge and momentum
relaxation. We then show how one can find the minimal relaxed hydrodynamic
framework that does yield two-point functions consistent with time-reversal
covariance. We claim the same approach naturally applies to boost agnostic
hydrodynamics and its limits (e.g. Carrollian, Galilean and Lifshitz fluids).
