Enables the transfer of a solute or solutes from one side of a membrane to the other according to the reaction: 3-sulfino-L-alanine (cysteinesulfinate) (out) + H+(in) + L-glutamate(in) = 3-sulfino-L-alanine(in) + H+(out) + L-glutamate(out).
3-sulfino-L-alanine: proton, glutamate antiporter activity