Two-dimensional superconductors, including twisted multilayer graphene, should exhibit a BKT transition, and the $T$-dependence of the superfluid stiffness should distinguish between nodal or gapped order parameter symmetries. This picture dramatically changes when spatially correlated disorder is taken into account. Such correlations naturally arise in moiré systems due to twist angle inhomogeneities, which we model using elasticity theory. Using a random impedance network based on realistic disorder in the local $T_c$, we show that such long-ranged inhomogeneities not only smear the BKT transition, but they can obscure the distinction between nodal and fully gapped superconducting order parameters. We propose that the real part of the conductivity can be used as a key diagnostic observable to probe the relevance of correlated disorder.