Not necessarily, considering how quickly so many Baby Boomer liberals fell away from being liberals after the '60s and '70s, and how quickly they fell into being conservative Reagan voters in the '80s. For the majority, their brand of liberalism was always about permissiveness rather than progressiveness, and the only ones they really cared about extending permissions for were themselves.
This is basically the entire Fox News demographic - rock-and-roll right-wingers.