We consider multiple quantum dots or molecular junctions 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
necessary and sufficient conditions for interference blockade also 
in the presence of spin-polarized leads. As an example we analyze a 
benzene single-electron transistor. For a setup with parallel
polarized leads, we show how to exploit the current blocking to 
selectively prepare the system in a defined spin state without 
application of any external magnetic field.