Explain how the 1960s, though often turbulent, were also very productive in creating the atmosphere for real change for women, blacks, Mexicans, Native Americans, etc.
This is undisputably true. The 1960s were very turbulent, with things like racial strife and the sexual revolution creating a much more chaotic society. However, this turbulence came along with new opportunities for the groups you mention.
For example, "the Pill" and the sexual revolution gave women the opportunity to become much more equal to men. Women who are in power now, like Hillary Clinton, are women who came of age during this time.
With regard to African Americans, this was the era of Civil Rights. The turmoil in the South led people all over the country to support the cause of civil rights. This led to the winning of legal equality in things like the Civil Rights Act of 1964 and the Voting Rights Act of 1965.