  We investigate the influence of general forms of disorder on the robustness
of superconductivity in multiband materials. Specifically, we consider a
general two-band system where the bands arise from an orbital degree of freedom
of the electrons. Within the Born approximation, we show that the interplay of
the spin-orbital structure of the normal-state Hamiltonian, disorder
scattering, and superconducting pairing potentials can lead to significant
deviations from the expected robustness of the superconductivity. This can be
conveniently formulated in terms of the so-called "superconducting fitness". In
particular, we verify a key role for unconventional $s$-wave states, permitted
by the spin-orbital structure and which may pair electrons that are not
time-reversed partners. To exemplify the role of Fermi surface topology and
spin-orbital texture, we apply our formalism to the candidate topological
superconductor Cu$_x$Bi$_2$Se$_3$, for which only a single band crosses the
Fermi energy, as well as models of the iron pnictides, which possess multiple
Fermi pockets.
