Many of those who came of age in the 60's represented the first large group of Americans to break free of the red scare, but it appears that these were only a minority with a large number of them falling back into the prevailing majority group think. Bernie Sanders is an exemplar of a person who came of age in the 60's who maintained his beliefs despite strong headwinds.
The propagandizing against socialism in that era helped Reagan gain power and influence, as it was only a short step from believing that American social programs were all too close in nature to the European social democrats who were too close to socialism etc. The other problem is that pursuing self-interest is perhaps the strongest human motivation, which feeds conservatism.
I think the age gap can only be overcome by waiting until fewer people who have been exposed to the propaganda and societal norms are around--maybe 10-20 years, unless there are exceptional circumstances. Trump's egregious behavior creates an opportunity, but it appears that a majority of Democratic voters strongly oppose or are afraid that others oppose strong government-based programs like M4A. Even Elizabeth Warren who I believe took a potentially effective approach in trying to combine strongly promoting capitalism with the same social programs as Bernie was defeated by moderate attacks on her "leftist" proposals--she had another problem in that she also had to overcome: sexism, which further weakened her candidacy.
In the near future, someone taking Warren's approach-- strongly promoting capitalism at the same time as promoting social democracy may be able to gain traction and unify the Democratic party as well as achieve a majority in the country.