American and world public opinion turned strongly in favor of the civil rights movement when

Martin Luther King's peaceful demonstrators were viciously attacked in Birmingham

Explanation:

In Birmingham in 1963 Martin Luther King Jr civil right demonstration was violently attacked, the aim of the demonstration was to protest against the segregation system within the system meted against the backs in the use of public facilities in Birmingham Alabama. The protest was lead by Martin Luther King, Reverend James Bevel, etc.