  We investigate the robustness against disorder of superconductivity in
multiband systems where the fermions have four internal degrees of freedom.
This permits unconventional $s$-wave pairing states, which may transform
nontrivially under crystal symmetries. Using the self-consistent Born
approximation, we develop a general theory for the effect of impurities on the
critical temperature, and find that the presence of these novel $s$-wave
channels significantly modifies the conclusions of single-band theories. We
apply our theory to two candidate topological superconductors, YPtBi and
Cu$_x$Bi$_2$Se$_3$, and show that the novel $s$-wave states display an enhanced
resilience against disorder, which extends to momentum-dependent pairing states
with the same crystal symmetry. The robustness of the $s$-wave states can be
quantified in terms of their superconducting fitness, which can be readily
evaluated for model systems.
