A key property of equilibrium exciton-polariton condensates in semiconductor microcavities is the suppression of the Zeeman splitting under a magnetic field. By studying magnetophotoluminescence spectra from a GaAs microcavity, we show experimentally that a similar effect occurs in a nonequilibrium polariton condensate arising from polariton parametric scattering. In this case, the quenching of Zeeman splitting is related to a phase synchronization of spin-up and spin-down polarized polariton condensates caused by a nonlinear coupling via the coherent pump state.