It seems like the end of the Amos 'n Andy show in the mid 1950s marks a turning point, and this is somewhat prior to the major non-violent protests that marked the "Civil Rights Era".
This is a good question, I think its important to understand that black face and racial discrimination are linked together.
The term Jim Crow comes from early 19th century Blackface minstrel shows, one of the most famous was Thomas Daddy Rice who devised a strutting dance character supposedly suggesting a prancing crow and the character that became known as Jim Crow. how did the character called Jim Crow became a general term for American racial discrimination is still not known but at some point in the 19th century the term ceased to have anything to do with minstrel shows and instead signified the practice of disfranchising and discriminating against African Americans.
The decline of Blackface began in the late 20s/ early 30s because of the popularly of the minstrel and vaudeville shows started to wane but also coincided with the rise of the NAACP as a civil rights org. By the 30s, The NAACP had finely tuned with a nationwide network of branches and a program that engaged black communities across country. what the NAACP lacked in resources it made up for in determinate individuals. This led to the NAACP escalated its lobbying and litigation efforts, becoming internationally known for its advocacy of equal rights and equal protection for the African Americans. These efforts increased public awareness of the issues of American Americans in the united states and led to shifts in public opinions and sharp decline in lynchings.
Still change toward blackface was slow and some performances persisted in to the 50s even with pressure from the civil rights movement.