In the late 1960s and early ’70s, the pro-choice side of the abortion debate frequently predicted that legal abortion would reduce single parenthood and make marriages more stable, while the pro-life side made the allegedly-counterintuitive claim that it would have roughly the opposite effect; overall, it’s fair to say that post-Roe trends were considerably kinder to Roe’s critics than to the “every child a wanted child” conceit.1 Conservatives (and not only conservatives) also made various “dystopian” predictions about eugenics and the commodification of human life as reproductive science advanced in the ’70s, while many liberals argued that these fears were overblown; today, from “selective reduction” to the culling of Down’s Syndrome fetuses to worldwide trends in sex-selective abortion, from our fertility industry’s “embryo glut” to the global market in paid surrogacy, the dystopian predictions are basically just the status quo.
Religious fears that population control would turn coercive and tyrannical were scoffed at and then vindicated. Dan Quayle was laughed at until the data suggested that basically he had it right. The fairly-ancient conservative premise that social permissiveness is better for the rich than for the poor persistently bemuses the left; it also persistently describes reality. And if you dropped some of the documentation from today’s college rape crisis through a wormhole into the 1960s-era debates over shifting to coed living arrangements on campuses, I’m pretty sure that even many of the conservatives in that era would assume that someone was pranking them, that even in their worst fears it couldn’t possibly end up like this.
More broadly, over the last few decades social conservatives have frequently offered “both/and” cultural analyses that liberals have found strange or incredible — arguing (as noted above) that a sexually-permissive society can easily end up with a high abortion rate and a high out-of-wedlock birthrate; or that permissive societies can end up with more births to single parents and fewer births (not only fewer than replacement, but fewer than women actually desire) overall; or that expressive individualism could lead to fewer marriages and greater unhappiness for people who do get hitched.
Unfortunately, in the context of your question it seems that the answer--for all of those--is still no. Perhaps there's an argument there that social conservatives have accurately predicted history, and they are exactly where they said they would be given a few concessions.