What DuBois is doing here is taking issue with Booker T. Washington's ideas about how blacks should make progress in the US.
In this quote, what he is saying is that the black race as a whole cannot possibly progress economically if it is relegated to second class citizenship on the political level. The phrase "servile caste" means a group of people who will be seen as slaves/servants of others.
Washington thought that blacks could progress economically and then get political rights. DuBois is saying this is impossible. Just after the part you quote, he will give his arguments as to why it is impossible.