Well, of course it was a mix of real-world science and fantasy science. Those "other-dimension" things were handwaves to acknowledge the real scientific problems with superpowers and work around them. For instance, explaining how shapeshifters violate conservation of mass by drawing matter from some other dimension. A truly unscientific approach wouldn't even mention the idea of conservation of mass. Of course most of this stuff is fanciful and impossible, but you can still approach it in a scientifically literate way by acknowledging the scientific laws and principles that would have to be worked around to make these powers possible, even if the workarounds are themselves purely imaginary. The goal of scientific literacy in speculative fiction is not to be slavishly bound by real science, it's to understand the rules of science well enough to make it sound convincing when you break them.
Chris Claremont and John Byrne were pretty good at this in X-Men. For instance, having Nightcrawler's teleportation be subject to conservation of momentum, so that he couldn't use it to save himself from falling because he'd still be falling at the same speed afterward. The ability itself was impossible, but aside from that it was bound by the normal laws of physics. And they explained the teleportation as passage through another dimension, which is itself a hypothetical scientific concept, even though it's often treated in a fanciful manner in fiction.
