At the Large Hadron Collider (LHC), absolute luminosity calibrations obtained by the van der Meer (vdM) method are affected by the mutual electromagnetic interaction of the two beams. The colliding bunches experience relative orbit shifts, as well as optical distortions akin to the dynamic-beta effect, that both depend on the transverse beam separation and must therefore be corrected for when deriving the absolute luminosity scale. In the vdM regime, the beam-beam parameter is small enough that the orbit shift can be calculated analytically. The dynamic-beta corrections to the luminometer calibrations, however, had until the end of Run 2 been estimated in the linear approximation only. In this report, the influence of beam-beam effects on the vdM-based luminosity scale is quantified, together with the associated systematic uncertainties, by means of simulations that fully take into account the non-linearity of the beambeam force, as well as the resulting non-Gaussian distortions of the transverse beam distributions. Two independent multi-particle simulations, one limited to the weak-strong approximation and one that models strong-strong effects in a self-consistent manner, are found in excellent agreement; both predict a percent-level shift of the absolute pp-luminosity values with respect to those assumed until recently in the physics publications of the LHC experiments. These results also provide guidance regarding further studies aimed at reducing the beam-beam-related systematic uncertainty on beam-beam corrections to absolute luminosity calibrations by the van der Meer method.