1960s was when the hypothesis of continental drift was empirically confirmed (leading to modern plate tectonics) but it was part of a prominent family of hypotheses (contending with isostatic models) more than a century prior.
The most complete of these models was offered by Wegener (paper in 1912, book in 1920). European geologists were generally receptive to it in the 1920s, and by the 1940s it was the working assumption for most field work. The only geologists to outright reject the idea initially were part of a North American contingent.
As to why Americans in particular, there were a few reasons, but a big one is that they didn’t read German and the first English edition of Wegener’s book was a draft-quality translation with issues relating to clarity and “tone.” The author was perceived to be dismissive of current work in the field (he was merely unaware of similar models offered previously) culminating in a summit seminar where a talk was given challenging the hypothesis and criticizing the methodology.
Interestingly, Wegener attended this talk, yet chose to remain silent. He never confirmed why. I would guess language barrier and shyness but I don’t know. Regardless, the matter was considered closed by those in attendance and his model’s acceptance by North American geologists lagged behind.
As a result, geology in American primary education saw the most dramatic curricular shift in the 1970s and 1980s. I suspect that’s why older Americans have this impression of a sudden change in scientific consensus. The true story is more interesting IMO.