  Recently it was shown that the topological properties of $2D$ and $3D$
topological insulators are captured by a $\mathbb{Z}_2$ chiral anomaly in the
boundary field theory. It remained, however, unclear whether the anomaly
survives electron-electron interactions. We show that this is indeed the case,
thereby providing an alternative formalism for treating topological insulators
in the interacting regime. We apply this formalism to fractional topological
insulators (FTI) via projective/parton constructions and use it to test the
robustness of all fractional topological insulators which can be described in
this way. The stability criterion we develop is easy to check and based on the
pairswitching behaviour of the noninteracting partons. In particular, we find
that FTIs based on bosonic Laughlin states and the $M=0$ bosonic Read-Rezayi
states are fragile and may have a completely gapped and non-degenerate edge
spectrum in each topological sector. In contrast, the $\mathbb{Z}_{k}$
Read-Rezayi states with $M=1$ and odd $k$ and the bosonic $3D$ topological
insulator with a $\pi/4$ fractional theta-term are topologically stable.
