We consider nanojunctions in the single-electron tunneling regime which, due to a high degree of spatial symmetry, have a degenerate many-body spectrum. As a consequence, interference phenomena which cause a current blocking can occur at specific values of the bias and gate voltage. We present here a general formalism to give necessary and sufficient conditions for interference blockade also in the presence of spin-polarized leads. As an example we analyze a triple quantum-dot single-electron transistor. For a setup with parallel polarized leads, we show how to selectively prepare the system in each of the three states of an excited spin triplet without application of any external magnetic field.