Thanks for the question. Very good observation.
I interpreted it to mean DuBois thinks Blacks will vote (those who can). It is 1956 and most Blacks can’t even vote legally at that time. However, he is saying that the two parties (GOP and Democrat) are corrupt and corporate owned and don’t do anything for anyone except themselves and their corporate masters. He is saying in 1956 the system was broken and was being run by one party even though they are positioned as two parties. That is pretty much the same complaint being made by many today. The part about Blacks wanting to vote I think he is saying they should vote though at the time most of us could not vote anyway. That has changed.