  We show that literature results claimed for the magnetic field dependence of
the longitudinal conductivity in anomalous first-order hydrodynamics are frame
dependent at this derivative order. In particular, we focus on
$(3+1)$-dimensional hydrodynamics in the presence of a constant ${\cal
O}(\partial)$ magnetic field with a $U(1)$ chiral anomaly and demonstrate that,
for constitutive relations up to and including order one in derivatives, the
anomaly drops out of the longitudinal conductivity. In particular, magnetic
field dependent terms that were previously found in the literature only enter
the non-zero frequency thermoelectric conductivities through explicitly frame
dependent pieces indicating that they are not physical. This issue can be
avoided entirely by incorporating the magnetic field into the fluid's
equilibrium state.
