Depends on whether or not we're talking about de jure or de facto rights.

In terms of de jure rights blacks had the same constitutional rights as white people. However in the south there were the Jim Crow state laws had put restrictions on his ability to vote (literacy tests or grandfather clauses) and there was segregation or public places and services.

However de facto rights complicated this greatly. Across America blacks would find their rights ignored or be put to inconvenience. Also segregation worked legally on the idea of separate but equal, in practise black services were given less money, made worse by low wages for black workers. Law enforcement was mainly made up of white people so both the police and courts were hostile to blacks.

Generally in the 1930's the civil rights movement is in its infancy and still focused on fighting small legal actions against specific laws, renting for example.