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They're using slide rule users as a stand-in for serious mathematician as opposed to people who incidentally use mathematics. It makes some sense in historical context but becomes a bit anachronistic after the invention of electronic calculators.

Slide-rule is a sort of "trope". If you need to signal to readers or your book or watchers of your movie that some character has STEM education, you give them a slide-rule. There are other ways to do this, you can make them wear white coats. White coat is more popular though, if the author used white coats, I'm sure you'd be able to get it.

I took it as being a tongue-in-cheek way of saying "mathematicians."