This is a textbook logical fallacy - post hoc ergo propter hoc, that is, "after that, therefore because of that." Just because something happens after a previous event does not mean that the prior event caused it. The decline in American society can be traced to other factors just as easily.
(Incidentally, I would dispute your dates. Evolution was taught in schools in the 1920's too.)
I'd think the introduction of The Pill, and the ready availability of automobiles had more to do with the slackening of morals in the 60s than any other causes.
Oh, I wouldn't debate that. Causal relationships don't need to be complex. In this case I don't believe it is. It's simple. It's like deciding to steal for the first time. The first time doesn't make one a master thief. And getting caught doesn't presuppose an end to the crime spree. The degeneration of societal norms of morality is arguably a staged affair that traces back through a number of steps and causalities. I just see this factor as the crack in the damn that blew. When you look at the data, the incidents start their climb at the same time evolution made it to the classroom and started calling God a liar, mom and dad a liar and all of mom and dad's church friends liars because 'we have the evidence'. Doesn't take kids too long to realize that if the creation story is being sold as a lie, the rest of that book ain't worth a plug nickel and what we decide to do doesn't matter in the scheme of things. Kids don't just make that leap overnight en masse without something culturally defining the excuse.