Well, from a personal point of view, it opened the door for American guys to start wearing their hair longer although in that time period it was the first time I can remember my mother ever laying a hand on me in anger: I refused to cut my hair. We began to question all those things that we had been raised to take for granted. And they were extremely turbulent times. Kids were being killed by military units at college campuses for protesting. Also, some of their political and social commetary was deliverd in a "harmonious" way.
With the popularity of their music came the ability to question the quid pro quo of the politics of America, American life in general, and the Vietnam war in particular. The "British Invasion" of music up to the advent of the Beatles was more gritty and dirty till the Beatles "seemed to give it a bath" while still managing to be social rebels. They helped make protest and social rebelion a more palitable and acceptable concept.