Boy, is this a trip down memory lane. I guess, to touch on my thoughts about the original question, it depends on whose version you like best. Mine was Peter, Paul and Mary's. I never cared for Dylan's voice. I was living in Chicago, right after the Democratic convention, and it was a truly remarkable place to be in. Richard Daley, the first, was mayor...and the Chicago police were like...well, storm troopers. To quote Dickens, It was the best of times; it was the worst of times.... I was fortunate enough not to get my head busted or myself, either, on any of the peace marches, sit-ins, picket lines, rallys, etc. I attended. Blowing in the Wind was just one of many anthems, we sung in between chants...but it seemed to be the one that transcended the generation gap that was extremely wide then. Maybe, as someone above said, because it was somewhat innocuous...i.e., old people didn't get it, so it could be safely sung sweetly when you were at churches trying to raise money for the peace movement. It is its ambiguity, I think, as well, as others have said, that keeps it current, no matter what the era...just as This Land is Your Land.
I want to thank the person who provided the YouTube link...I attended three PPM concerts in Chicago between '68 and '72, and they were very much like the ones portrayed. Judy Collins and Joni Mitchell, too. Was, still am a big Joan Baez fan, as well as the others, too. I think PPM's Great Mandala, I think that's the title, was a stronger anti-war anthem, but Blowing... has stood the test of time, and more people relate to it. I do think you had to have been there.
Before the Vietnam War, people on the U.S. mainland only heard about war from the radio, newspapers, or relatives, friends who'd been there. We ate the images on television for dinner! (Sorry, I forgot newsreels.) Did we accomplish anything? The answer, my friends, is blowin' in the wind...