Question

What specifically was Dr. Martin Luther King Jr. speaking out against when he made this statement in 1958? “I could never adjust to the separate waiting rooms, separate eating places, separate rest rooms, partly because the separate was always unequal, and partly because the very idea of separation did something to my sense of dignity and self-respect.”
civil disobedience
the Montgomery Bus Boycott
the march on Selma, Alabama
Jim Crow laws
integration of public schools

Answer 1

Dr. Martin Luther King Jr. was specifically speaking out against the Jim crow Laws when he made that statement in 1958.

Answer 2

4) Jim Crow laws

Jim Crow laws were a series of restrictions that enforced racial segregation in the United States. They were enacted especially in the Southern States of America through almost a century, from 1877 to the beginning of the Civil Right Movement in the 1950s,

The statutes prohibited African American to attend and be in certain places where white people were, such as neighborhoods, restrooms, building entrances, elevators, cemeteries, amusement-park, cashier windows, churches, hospitals, jails, universities, etc.

In the speech, Dr. Martin Luther King Jr. is clearly talking about these laws, because though in theory the racial segregation was supposed to be "equal" for both races, in practice, the laws were never equal, black people never enjoyed the same benefits that white people enjoyed, and the laws put African American in a place of inferiority and made them uncomfortable.