I must not hang out in the right circles, because I haven’t seen that enough to see it as a cliché.

Possibly. Give it time I suppose

Perhaps the commenter was not dismissing multiverse theory because of a gut reaction, but because they’re fed up themselves with popular and un-falsifiable speculation being treated as science.

Perhaps, but you'd have a hard time tying to convince Princeton University that the the paper they gave Hugh Everett a PhD in Physics for is in fact "not science" and is in fact more like "the boogey man or the tooth fairy." Or trying to convince the scientific community that people like Sean Carroll and David Deutsch and all the other physicists doing work in Quantum Foundations from a many worlds perspective aren't scientists.

this “spooky action at a distance” that famous pre-redditor Albert dismissed as nonsense.

I'm sorry, but this is just straight up not true; Einstein absolutely did not dismiss entanglement as nonsense

But there’s a gap between that science and the interpretations of it.

Different "interpretations" (really they are different theories) absolutely have experimental differences. Some aren't performable today, but if that is your criteria, then the Higgs Boson was like the tooth fairy for decades. But even beyond that some are performable, and have been performed, we have done test for dynamical collapse interpretations. Had they come back positive they would have falsified Many Worlds, ie. they are literally a form of falsification.

And maybe coming from they popular end, it’s easy to see the wilder speculations as nothing more than unprovable imagination.

And many worlds is not one of those wilder speculations that is nothing more than unprovable imaginations.

that itself takes time and logic and mathematics… it takes science!

Indeed, which means not dismissing and idea as nonsense without understanding it.