When stymied by executive and legislative inaction where did the civil rights activists turn for support?

If the legislative and executive branches of government aren't helping your cause, which branch of government is left?  The judicial branch.  The courts of the United States began to play a larger and larger role in affirming equal rights for all citizens regardless of race.  Civil rights activists staged marches and sit-ins and took seats on buses and in restaurants that society said they weren't entitled to have.  So the civil rights activists did a lot to press their own cause in their own ways.  But as far as government goes, the defense of civil rights came first from court decision such as Brown vs. the Board of Education (1954) which ruled that segregated schools are unconstitutional, and Loving vs. Virginia (1967) which ruled that laws prohibiting interracial marriage are unconstitutional.