  Two-dimensional materials are a highly tunable platform for studying the
momentum space topology of the electronic wavefunctions and real space topology
in terms of skyrmions, merons, and vortices of an order parameter. Such
textures for electronic polarization can exist in moir\'e heterostructures. A
quantum-mechanical definition of local polarization textures in insulating
supercells was recently proposed. Here, we propose a definition for local
polarization that is also valid for systems with topologically non-trivial
bands. We introduce semilocal hybrid polarizations, which are valid even when
the Wannier functions in a system cannot be made exponentially localized in all
dimensions. We use this definition to explicitly show that nontrivial
real-space polarization textures can exist in topologically non-trivial systems
with non-zero Chern number under (1) an external superlattice potential, and
(2) under a stacking-induced moir\'e potential. In the latter, we find that
while the magnitude of the local polarization decreases discontinuously across
a topological phase transition from trivial to topologically nontrivial, the
polarization does not completely vanish. Our findings suggest that band
topology and real-space polar topology may coexist in real materials.
