  The emergence of correlated insulating phases in magic-angle twisted bilayer
graphene exhibits strong sample dependence. Here, we derive an Anderson theorem
governing the robustness against disorder of the Kramers intervalley coherent
(K-IVC) state, a prime candidate for describing the correlated insulators at
even fillings of the moir\'e flat bands. We find that the K-IVC gap is robust
against local perturbations, which are odd under $\mathcal{PT}$, where
$\mathcal{P}$ and $\mathcal{T}$ denote particle-hole conjugation and time
reversal, respectively. In contrast, $\mathcal{PT}$-even perturbations will in
general induce subgap states and reduce or even eliminate the gap. We use this
result to classify the stability of the K-IVC state against various
experimentally relevant perturbations. The existence of an Anderson theorem
singles out the K-IVC state from other possible insulating ground states.
