Even with no Vietnam war, I suspect all the young people with money and leisure time and an educational system which constantly reminds them that they are the generation which will bring about The Glorious Future will raise a fuss about _something_: the civil rights issue, which certainly mobilized a lot of people OTL, or the whole "older generation saddled us with the threat of nuclear annihilation" thing, which isn't going away. There will be a "youth culture", driven by marketing if nothing else, and it won't look like the 50's: could end up rather different from our 60's, though.
Bruce