  Axions and other light particles appear ubiquitously in physics beyond the
Standard Model, with a variety of possible couplings to ordinary matter.
Cosmology offers a unique probe of these particles as they can thermalize in
the hot environment of the early universe for any such coupling. For sub-MeV
particles, their entropy must leave a measurable cosmological signal, usually
via the effective number of relativistic particles, $N_\mathrm{eff}$. In this
paper, we will revisit the cosmological constraints on the couplings of axions
and other pseudo-Nambu-Goldstone bosons to Standard Model fermions from
thermalization below the electroweak scale, where these couplings are marginal
and give contributions to the radiation density of $\Delta N_\mathrm{eff} >
0.027$. We update the calculation of the production rates to eliminate
unnecessary approximations and find that the cosmological bounds on these
interactions are complementary to astrophysical constraints, e.g. from
supernova SN 1987A. We additionally provide quantitative explanations for these
bounds and their relationship.
