  Using comprehensive exact diagonalization calculations on $\theta \approx 3.7
^{\circ}$ twisted bilayer MoTe$_2$ ($t$MoTe$_2$), as well as idealized Landau
level models also relevant for lower $\theta$, we extract general principles
for engineering fractional topological insulators (FTIs) in realistic
situations. First, in a Landau level setup at $\nu=1/3+1/3$, we investigate
what features of the interaction destroy an FTI. For both pseudopotential
interactions and realistic screened Coulomb interactions, we find that
sufficient suppression of the short-range repulsion is needed for stabilizing
an FTI. We then study $\theta \approx 3.7 ^{\circ}$ $t$MoTe$_2$ with realistic
band-mixing and anisotropic non-local dielectric screening. Our finite-size
calculations only find an FTI phase at $\nu=-4/3$ in the presence of a
significant additional short-range attraction $g$ that acts to counter the
Coulomb repulsion at short distances. We discuss how further finite-size
drifts, dielectric engineering, Landau level character, and band-mixing effects
may reduce the required value of $g$ closer towards the experimentally relevant
conditions of $t$MoTe$_2$. Projective calculations into the $n=1$ Landau level,
which resembles the second valence band of $\theta\simeq 2.1^\circ$
$t$MoTe$_2$, do not yield FTIs for any $g$, suggesting that FTIs at low-angle
$t$MoTe$_2$ for $\nu=-8/3$ and $-10/3$ may be unlikely. While our study
highlights the challenges, at least for the fillings considered, to obtaining
an FTI with transport plateaus, even in large-angle $t$MoTe$_2$ where
fractional Chern insulators are experimentally established, we also provide
potential sample-engineering routes to improve the stability of FTI phases.
