They got more conservative as they got older. All those hippie kids who protested Vietnam and experimented with drugs and sex ended up voting for Reagan.
People seem to have this view that everyone in the '60s was a hippie but that's just not true. Time Magazine put the number around 300,000. In a country of 200 million, that's only 0.15% of the population. They were a counterculture not mainstream culture. The vast majority of kids did not become hippies, and many actively hated the hippies.
You have 4 people, 3 liberals and 1 conservative, graduating from high school at 18, 75% are liberal. When they are in their late 30s, one of the liberals dies, so 66% are liberals. Then at age 50 another liberal dies, so the group is 50% liberal. One year after retirement (65) the last liberal dies and now the entire cohort is conservative. Without looking at the size of the population, one would think that the group of 4 slowly became more conservative over time.
Death, not persuasion, causes the political leaning of the population to shift as they get older. It is the very concerns of those that are liberal which also lead to their earlier deaths. If you are less likely to die from something that can be fixed with politics, you are more likely to be conservative and not want to rock the boat.
It turns out that the media jumped all over things like Hippies and anti-war protests. In reality, the average person was just as conservative then as they were 10 - 20 years ago.