  The fermionic minimal models are a recently-introduced family of
two-dimensional spin conformal field theories. We determine all of their
conformal boundary states and potentially anomalous $\mathbb{Z}_2$ global
symmetries. The latter task hinges upon on a conjecture about
$\mathfrak{su}(2)$ affine parities generalising an earlier result known to have
an interpretation in terms of Fermat curves. Our results indicate a close
connection between several properties of the models, including the matching of
the sizes of the SPT classes of boundary states, the existence of anomalous
$\mathbb{Z}_2$ symmetries, and the vanishing of the Ramond-Ramond sector, for
which we provide an explanation.
