C points, circular polarization in momentum space, play crucial roles in chiral wave manipulations. However, conventional approaches of achieving intrinsic C points using photonic crystals with broken symmetries suffer from a low Q factor and high sensitivity to structural geometry, rendering them fragile and susceptible to perturbations and disorders. We report magneto-optical (MO) bound states in the continuum (BICs) with a symmetry-preserved planar photonic crystal. We achieve intrinsic C points at Γ point that are robust against variation in both structural geometry and external magnetic field. MO coupling between two modes induces Zeeman splitting, leading to MO BICs and quasi-BICs with circular eigenstates for high-Q chiral responses. Furthermore, switchable C point handedness and circular dichroism are enabled by reversing the magnetic field. These findings unveil BICs and quasi-BICs with circular eigenstates and on-demand control of C points, paving the way for advanced chiral wave manipulation with enhanced light-matter interaction.