  We study constraints on the space of $d=2$ fermionic CFTs as a function of
non-perturbative anomalies exhibited under a fermionic discrete symmetry group
$G^f$, focusing our attention also on cases where $G^f$ is non-abelian or
presents a non-trivial twist of the $\mathbb{Z}^f_2$ subgroup. For the cases we
selected, among our results we find that modular bootstrap consistency bounds
predict the presence of relevant/marginal operators only for some groups and
anomalies. From this point of view, the appearance in the analysis of several
kinks around irrelevant operators with $\Delta>2$ means that for fermionic
systems with increasingly larger symmetry groups modular bootstrap is able to
give less constraining bounds than its bosonic counterpart. Within our analysis
we show how the anomaly constraints on fermionic CFTs can be effectively
recovered from the structure of the abelian subgroups of $G^f$. Finally, we
extend the previous surgery description of bordism invariants that describe
$3d$ abelian spin-TQFTs, in order to include the case of theories with
$\mathrm{Spin}\text{-}\mathbb{Z}^f_{2^{l+1}}$ structures.
