  Motivated by the recent discovery of superconductivity in the kagome
$A$V$_3$Sb$_5$ ($A$: K, Rb, Cs) metals, we perform a theoretical study of the
symmetry-allowed superconducting orders on the two-dimensional kagome lattice
with focus on their response to disorder. We uncover a qualitative difference
between the robustness of intraband spin-singlet (even-parity) and spin-triplet
(odd-parity) unconventional superconductivity to atomic-scale nonmagnetic
disorder. Due to the particular sublattice character of the electronic states
on the kagome lattice, disorder in spin-singlet superconducting phases is only
weakly pair-breaking despite the fact that the gap structure features sign
changes. By contrast, spin-triplet condensates remain fragile to disorder on
the kagome lattice. We demonstrate these effects in terms of the absence of
impurity bound states and an associated weak disorder-induced $T_c$-suppression
for spin-singlet order. We also discuss the consequences for quasi-particle
interference and their inherent tendency for momentum-space anisotropy due to
sublattice effects on the kagome lattice. For unconventional kagome
superconductors, our results imply that any allowed spin-singlet order,
including for example $d+id$-wave superconductivity, exhibits a
disorder-response qualitatively similar to standard conventional $s$-wave
superconductors.
