  Recently several moir\'e super-lattice systems are proposed to host nearly
flat $\pm$ Chern bands: the bands of the two valleys have opposite Chern
numbers. In these systems the charge of each valley is separately conserved.
For the $C=\pm 1$ case, in the perfect flat band limit, the system can be
mapped to two Landau levels from opposite magnetic fields. Motivated by these
promising experimental realizations, we consider a quantum Hall bilayers from
opposite magnetic fields close to the filling $\nu_T=\frac{1}{2}+\frac{1}{2}$.
We add inter-layer repulsive interaction starting from two decoupled Composite
Fermion Liquids (CFL) with opposite chiralities. In this case physical exciton
is frustrated from condensation, unlike the conventional quantum Hall bilayers.
We argue that more natural phases are the exciton condensates between composite
fermions or between slave bosons. The resulting states are insulators with
neutral Fermi surfaces coupled to an emergent $U(1)$ gauge field without
Chern-Simons term. This insulating state is a generalization of the well-known
CFL state and may potentially emerge in the moir\'e systems with $C=\pm 1$
narrow bands. Finally we also comment on the possibility of a topological
superconductor from charge frustration in opposite-fields quantum Hall bilayers
or in $C=\pm 1$ flat bands.
