For argument's sake, let's say we get an American generation that looks like the Mods. That they're just as anti-war and into free love [if you have the invention of the Pill, nothing's going to stop that] but they dress much more conservatively. And for further argument's sake, we're taking about kids who are mostly white and middle class.
For one thing, you're not going to get as much of a conservative backlash. Someone wearing a suit and tie - however stylish - is going to raise a lot of less ire than a twenty-year-old in beads and sandals. And someone droning on about Camus and the French new wave film they just saw will simply attract less attention than dancing about barefoot on the streets of San Francisco.
Jazz might stay a lot more popular. And lastly, if they've superficially bought more into the system, the young and the unions might be able to build the alliance they never were able to achieve in this reality.