A spin-Meissner effect occurs when the photoluminescence energy is dependent on interactions of otherwise magnetically sensitive particles. Under such a condition, the Zeeman energy splitting becomes zero when the chemical potentials for individual spin components of a spinor polariton condensate are equal or synchronized. Herein, we explore the types of topological spin-Meissner (TSM) states in the formation of a spinor dark soliton in semiconductor microcavities. The effects of nonlinear spin-anisotropic interactions between polaritons, spinflipping rate from the introduced defects, and energy splitting are theoretically investigated. We observe that, below a critical energy splitting for a given pump power, multistable TSM states exist. However, above a critical energy splitting, the two spin components of the dark soliton pair become desynchronized.