Having gotten us deeply into the Vietnam war, the Democrats joined the "peace" movement* only after a hated Republican took the presidency and they could use the war as a political bludgeon on him.
The media set the narrative that Nixon could either lose the war and be blamed for it, or keep fighting an unwinnable war in which our side opposed democracy.
In my opinion, we don't have a viable peace movement now, not because today's music sucks so bad (and it surely does), but because both parties are so firmly in the pockets of the arms manufacturers.