  We show that in theories of axionlike particles (ALPs) coupled to electrons
at tree-level, the one-loop effective coupling to photons is process dependent:
the effective coupling relevant for decay processes,
$g_{a\gamma}^{\text{(D)}}$, differs significantly from the coupling appearing
in the phenomenologically important Primakoff process,
$g_{a\gamma}^{\text{(P)}}$. We show that this has important implications for
the physics of massive ALPs in hot and dense environments, such as supernovae.
We derive, as a consequence, new limits on the ALP-electron coupling,
$\hat{g}_{ae}$, from SN 1987A by accounting for all relevant production
processes, including one-loop processes, and considering bounds from excess
cooling as well as the absence of an associated gamma-ray burst from ALP
decays. Our limits are among the strongest to date for ALP masses in the range
$0.03 \, \text{MeV} \, < m_a< 240 \, \text{MeV}$. Moreover, we also show how
cosmological bounds on the ALP-photon coupling translate into new, strong
limits on $\hat{g}_{ae}$ at one loop. Our analysis emphasises that large
hierarchies between ALP effective couplings are difficult to realise once
quantum loops are taken into account.
