Question

In the late 1960s, what did members of the counterculture share with many other American citizens?

Answer 1

There could be several options for this, but the best would be that both the members of the counterculture and other Americans shared an aversion to the war it Vietnam, which they thought was wasting US lives. 

Answer 2

In the late 1960s, both members of countercultural movements and American society in general, came together to convey their desire to end the Vietnam War.

While initially the hippie counterculture movement was the one that triggered the protests, soon the results of the war ended up unifying the entire American society under the same thought. The pacifist movement saw the participation of students, mothers of soldiers, African-Americans, hippies, educators, religious, academics, journalists, lawyers, doctors, military veterans and in general all the factions of the American society of the time.