We propose an approach for the excitation of polariton Tamm states with a controllable nontrivial topology. The Tamm polaritons emerge at the interface of two binary one-dimensional photonic crystals belonging to a C3v point group, with an exciton resonance within their matching band gaps. The external magnetic field applied in the Faraday geometry endows the dispersion of the Tamm polaritons with the nonreciprocity: it lifts the degeneracy between opposite propagation directions in the interface plane. The phenomenology of Tamm polariton currents closely resembles one of a Z2 topological insulator. The proposed structure acts as an optical spin splitter controlled by the magnetic field magnitude.