  Motivated by a recent experiment reporting the fractional quantum spin Hall
effect in twisted ${\rm MoTe}_2$, we investigate microscopically the prospects
of realizing exotic topologically ordered states beyond conventional quantum
Hall physics. We show that a non-Abelian spin Hall insulator, a state of two
copies of the non-Abelian Moore-Read state, can be stabilized at half filling
of time-reversal conjugate Chern bands. We elucidate that the existence of this
phase relies on the reduction of opposite-spin interactions at short distances
to overcome the Ising ferromagnetism. Moreover, we demonstrate that band mixing
provides a generic mechanism for this reduction to be achieved. Quite
remarkably, we find that a renormalization of opposite-spin interactions at
short distances as small as 15 % of the moir\'e period is sufficient for a
direct transition to a completely spin unpolarized phase which supports the
non-Abelian spin Hall insulator. Furthermore, we show that the non-Abelian spin
Hall insulator can either break time-reversal symmetry or preserve it depending
on the underlying topological order.
