I thought the opposite: the writers of the original Star Trek seemed to think nothing of including teleportation, nor does it cause alarm in D&D/Planescape or Harry Potter.

I'm not sure how this is evidence for your hypothesis 'the objection you point to stemmed from a false understanding of physics that made "physical continuity" important'. If you are right, wouldn't this false understanding of physics also apply to Star Trek (which is supposed to have the same physics as our world), and lead to the same objection? I think a more likely explanation is that for various reasons, the the details of how transporters are supposed to work and the implications thereof don't rise to salience in most viewers' minds.

In the case of D&D/Planescape and Harry Potter, I think the supposed physics/ontology of the fictional worlds are different enough from ours (they both have actual souls for example) and also sufficiently murky that we just say "if the in-world characters aren't worried about their teleportation spells, who am I to judge?"