How widespread was opposition to continental drift at the time?

I can't particularly speak to the religious opposition of continental drift the 1980s and 1990s you experienced beyond more general skepticism of deep time [1], vis-a-vis Young Earth Creationism, but continental drift, along with related fundamental geophysical facts, was generally accepted later than you might anticipate.

That the Earth was ancient was known in the 18th century; several scientists proposed dates over the course of the 18th and 19th centuries, most notably Lord Kelvin and Charles Lyell, with Lord Kelvin on the side of the physicists who calculated an age of around 20 million years (though he did propose numbers as high as 100 million) and Lyell for the geologists and paleontologists, who believed that evolution would have taken many tens of millions of years, and possibly even hundreds of millions. At the turn of the century, a younger age in the low tens of millions was generally accepted; by the 1920s, with the discovery of radiometric dating and then its solidification by Arthur Holmes in 1927, it was known that the earth was billions of years old. Finally, Clair Cameron Patterson calculated an age of 4.5 billion years based on the Canyon Diablo meteorite in the mid-1950s.

Against this backdrop came continental drift. While earlier thinkers did contend with the apparent shape continuity of continents, most notably Alexander von Humboldt, modern continental drift is attributed to Alfred Wegener. The mechanism that Wegener proposed in the 1910s, Polflucht--that centrifugal forces would draw landmasses toward the equator--was readily rejected by most contemporary geophysicists: the numbers simply didn't make sense. The forces involved are too small, while Wegener's proposed rate of drift too high. The age of the earth itself was in flux, but none of Wegener's early numbers meshed with what was known (either too old or too young). Arthur Holmes embraced a modified version of continental drift in the 1920s, but generally found skepticism throughout the 1920s and 1940s. Only in the late 1950s and early 1960s were the "zebra stripe" ocean floor magnetization patterns discovered in the 1940s connected to continental drift: from the Great Rift, magma that would eventually become landmasses was being churned out, thus creating matching 'stripes' due to geomagnetic reversals. The Vine-Mathews-Morley hypothesis for seafloor spreading was crystallized in 1963, and the theory of plate tectonics was generally accepted by the late 1960s after further refinement.

Scientifically, by 1970 there wasn't much debate over plate tectonics. Culturally, just as we still have public debates over the age of the earth, plate tectonics and continental drift have found opposition. It appears the Institute for Creation Research maintains that plate tectonics is "doubtful"; nonetheless, a recent survey showed that plate tectonics is more accepted than heliocentricity, so it has definitely not drawn the sort of attention that evolution or deep time has.

Students who attended school or university in the 1940s and early 1950s would likely have not been taught plate tectonics or continental drift, and if they were it would be unlikely for it to be presented positively--we might equate it to something like the Solutrean Hypothesis in the 1970s and 1980s.

So it is definitely plausible for a teacher in the 1980s or 1990s to hold doubts or (measured?) opposition to plate tectonics given the science they would have been taught--indeed the finer mechanisms of plate tectonics aren't known even today. But I can't really imagine yelling and shouting over scientific disagreements see that sort of response in this context; instead, the religious valence lends credence to the rejection of continental drift here being YEC-associated skepticism of the deep time required for continental drift, as North America broke off from Eurasia 60 million years ago, and Africa/South America separated over 100 million years ago.

Edit:

Per /u/Killfile, which I had missed when drafting the answer:

As such, I would like to request that whomever delivers an answer within the expectations of the sub also address the phenomenon of shifting consensus in science/education more broadly.

Shifting scientific consensus in science is rather different than in education; neo-Darwinism was broadly accepted by the mid-1940s, for example, but adjudicated in the US for public school instruction in 1987 in response to a law in Louisiana that maintained creationism must be taught alongside neo-Darwinian evolution. A thorough response to scientific consensus change is probably outside the scope of the forum, but I would likely start from Kuhn's Structure of Scientific Revolutions, which holds that paradigms (generally accepted scientific beliefs, e.g. that the tectonic plates themselves are static) buckle under the accumulation of aberrations, leading to a paradigm shift. This isn't a teleological progression toward truth; rather, a paradigm shift simply demarcates a new consensus. The bacterial theory of ulcers is a classic example of adirectional paradigm shifts, where the belief the H. pylori bacteria cause ulcer was proposed, rejected in favor of alternative paradigms, and ultimately accepted; arguably plate tectonics occupies this same role.

I am afraid I can not speak in greater depth on education except to highlight the political lens of public schools as well as the lag between novel scientific research -> consensus -> teacher training and textbook adoption.

1: The historicity of the earth was recognized over the course of the 17th and 18th centuries, in a chronological tradition that arose from the same ecclesiastical scholarship that serves as the basis for YEC. Martin Rudwick's Bursting the Limits of Time and Worlds Before Adam are wonderful books on the recognition of deep time.

Mazur, Allan. "Do Americans believe modern earth science?." Evolution: Education and Outreach 3, no. 4 (2010): 629-632.