We theoretically investigate the charge and spin transport through a binuclear (FeFeIII)-Fe-III iron complex connected to two metallic electrodes. During the transport process, the (FeFeIII)-Fe-III dimer undergoes a one-electron reduction (Coulomb blockade transport regime), leading to the reduced mixed-valence (FeFeIII)-Fe-II species. For such a system, the additional electron may be fully delocalized leading to the stabilization of the highest spin ground state S = 9/2 by the double exchange mechanism, while the original (FeFeIII)-Fe-III has usually an S = 0 spin ground state due to the antiferromagnetic exchange coupling between the two Fe-III ions. Intuitively, the spin delocalization within the mixed-valence complex may be thought to favor charge and spin transport through the molecule between the two metallic electrodes. Contrary to such an intuitive concept, we find that the increased delocalization leads in fact to a blocking of the transport, if the exchange coupling interaction within the (FeFeIII)-Fe-III dimer is antiferromagnetic. This is due to the violation of the spin angular momentum conservation, where a change of half a unit of spin (Delta S = 1/2) is allowed between two different redox states of the molecule. The result is explained in terms of a double-exchange blockade mechanism, triggered by the interplay between spin delocalization and antiferromagnetic coupling between the magnetic cores. Consequently, ferromagnetically coupled dimers are shown not to be affected by the double-exchange blockade mechanism. The situation is evocative of the onset and removal of giant magnetoresistance in the conductance of diamagnetic layers, as a function of the relative alignment of the magnetization of two weakly antiferromagnetically coupled ferromagnetic contacts. Numerical simulations accounting for the effect of vibronic coupling show that the spin current increases as a function of spin delocalization in Class I and Class II mixed-valence dimers. The signature of vibronic coupling on sequential spin-tunneling processes through Class I and Class II mixed-valence systems is identified and discussed.