Context. Mutual neutralization (MN) between cations and anions plays an important role in determining the charge balance in certain astrophysical environments. However, empirical data for such reactions involving complex molecular species have been lacking due to challenges in performing experimental studies, leaving the astronomical community to rely on decades-old models with large uncertainties for describing these processes in the interstellar medium.Aims. Our aim is to investigate the MN reaction C60+ + C60− → C60* + C60 for collisions at interstellar-like conditions.Methods. We studied the MN reaction between C60+ and C60− at collision energies of 100 meV using the Double ElectroStatic Ion Ring ExpEriment (DESIREE) and its merged beam capabilities. To aid in the interpretation of the experimental results, semiclassical modeling based on the Landau-Zener approach was performed for the studied reaction.Results. We experimentally identified a narrow range of kinetic energies for the neutral reaction products. Modeling was used to calculate the quantum state-selective reaction probabilities, absolute cross sections, and rate coefficients of these MN reactions, using the experimental results as a benchmark. We compared the MN cross sections with model results for electron attachment to C60 and electron recombination with C60+.Conclusions. Our results show that it is crucial to take mutual polarization effects, the finite sizes, and the final quantum states of both molecular ions into account in order to obtain reliable predictions of MN rates expected to strongly influence the charge balance and chemistry in environments such as dense molecular clouds.