Liberty requires a responsible citizenry, and the sexual revolution (very much like the drug culture, which was and is its Doppelgänger) promotes irresponsibility of every kind. It promotes dependence, and it fosters an ethos in which those who exercise the virtues fostered by the market are punished for doing so and in which those who live for present pleasure are rewarded.
This is the way conservatives tend to view the cultural legacy of the 1960s. Along the civilization-barbarism axis, they view it as a slide from civilization toward barbarism.
Of course, progressives see it entirely differently. Along the oppressor-oppressed axis, they view the cultural changes as favorable, because women were liberated (a conservative would put scare quotes around “liberated”).
Along the libertarian’s coercion-freedom axis, the picture is mixed. On net, did the cultural changes lead to more or less government coercion? It is hard to say. For example, in the area of Civil Rights, I would argue that getting rid of Jim Crow laws reduced government coercion. (Note that in the early 1960s, prominent libertarians tended to take the states’ rights position, which strikes me as misguided.) However, there is a sense in which today government is overly intrusive on matters of race. (You may be happy with that if your concern is with the oppressor-oppressed axis, and you believe that government is helping the oppressed.) I would prefer that government model treating people as individuals by refusing to classify people by race (You may be very unhappy with my suggestion if you think that the oppressor-oppressed model is significant).
What to think of the unwed mother? To a conservative, she represents a slide down the slope away from civilization. To a progressive, she represents the oppressed “single mom.” To a libertarian, she represents someone who has made a choice. I think that conservatives and libertarians would agree that the state should not be the substitute father. However, it is quite a stretch to suggest that undoing the cultural revolution ought to be on the libertarian agenda.