We report on Hybrid Monte Carlo simulations at finite spin density of the p-band electrons in monolayer graphene with realistic interelectron interactions. Unlike simulations at finite charge-carrier density, these are not affected by a fermion-sign problem. Our results are in qualitative agreement with an interaction-induced warping of the Fermi contours and a reduction of the bandwidth as observed in angle-resolved photoemission spectroscopy experiments on charge-doped graphene systems. Furthermore, we find evidence that the neck-disrupting Lifshitz transition, which occurs when the Fermi level traverses the van Hove singularity (VHS), becomes a true quantum phase transition due to interactions. This is in line with an instability of the VHS toward the formation of ordered electronic phases, which has been predicted by a variety of different theoretical approaches.