The proper question is "What became apparent after the mid-1960s" - the mid-sixties was the point at which longer-term changes became unambiguously visible and increasingly dominant; it was the watershed.
The first answer to what happened is that from the mid-60s apostasy from Christianity became dominant - the West became mostly, then almost entirely, secular in its public discourse; then anti-Christian.
But this invites the question why? Why did the West abandon Christianity after all these centuries?
Or rather what for? For what did the West abandon Christianity?
The single word answer is SEX.
With the sexual revolution, in all its emerging facets - still ongoing and expanding - the Left (that is to say, fundamentally, organized anti-Christianity; and secondarily the forces of destruction unleashed by the end of Christianity), after trail and error with economics, meritocracy, egalitarianism etc. discovered its most powerful weapon: sex.
So what happened in the 1960s was the sexual revolution, and the purpose driving the sexual revolution was the destruction of Christianity and its removal from public discourse. And the reason for this is that the Left is anti-Christian.
And the reason for this is that the Left is anti-Good (i.e. evil); and knows that religion is the only effective long-term defense of the Good.
After the sexual revolution had done its work on Christianity, the Left was free to embark upon wide ranging destruction of anything and everything good, traditional, useful, long-termist - and most of all the multi-method destruction of the family - which is where we are now.
But the sexual revolution is at the root of it all. While that dominates, so does the Left, so does destruction.
Note: when I say the Left is evil, I am not - in general- referring to Leftists. Everybody mixes good and evil and the balance or predominance is ard to discern and impossible to measure. I mean that Leftists are servants of evil, work to promote evil; they themselves, taken as detached individuals, might be kind and well behaved; and those who serve the Good might be less kind, less well-behaved - but THAT is not the point.