During this period, was there a broad agreement on how to pursue a civil rights agenda?
It is not clear from this question which era you are asking about. However, it is safe to say that there was never a complete consensus among civil rights leaders as to how to pursue a civil rights agenda. Let us look at two examples of how this is true.
In the late 1800s and early 1900s, there was a major dispute between Booker T. Washington and W.E.B. Du Bois as to how African Americans should pursue rights. Washington advocated a fairly non-confrontational approach. He wanted African Americans to defer to whites, behave modestly and industriously, and assume that whites would eventually grant them rights out of respect for their actions. Du Bois, by contrast, wanted to push for legal equality in the near term.
In the era of the Civil Rights Movement, there were many different visions of how to pursue civil rights. Most famously, there was the split between Martin Luther King, Jr, and his followers and the “Black Power” movement. King wanted to push in a fairly conciliatory way for integration. The Black Power movement wanted to be much more aggressive and was also more inclined to push for black nationalism and separatism.
In other words, there have typically been disputes among civil rights leaders as to how to pursue their agenda.