Thermal (300 K) ion–molecule reaction rates are measured, using the µSR (muon spin rotation) technique, for the muonated rare gas molecular ions HeMu⁺ and NeMu⁺ reacting with NO, O₂, N₂O, NH₃, CF₄, C₂H₄, TMS, and CH₃NO₂. In almost every case (excepting O₂), both charge transfer (k_e) and muon transfer (k_µ) contribute to the reaction rate. Reaction is believed to occur from ro-vibrational excited states, [HeMu⁺]* and [NeMu⁺]*, due to the poor efficiency of He and Ne moderators for collisional deactivation. The total experimental rate constants, k_exp = k_µ + k_e, are generally in excellent agreement with total capture rates predicted by the simple ADO theory, regardless of the degree of internal excitation. Comparisons with literature values for corresponding protonated ion reaction rates with O₂ and C₂H₄ reveal little or no isotope effect, although it is noted that these reactions are dominated by proton transfer, in contrast to the µSR results.