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Wouldn't such a network filter also trigger on random (in the sense of unpredictable to the reader) pages here on HN though? Or Reddit, etc?

I've never lived under such a regime, but all of the trigger words I can imagine at OP's site are also present in generally-SFW discussion forums.

Yeah but the IT bod looking into it would see the rest of the site as context

If they check on a site and it's heavy on the NSFW maybe things get looked into with a bit more of a "... is this person browsing porn at work?" attitude

Good point. I have never suffered such indignity, but I forget my privilege.

This is 100% the correct answer. It’s unfortunate nsfw was framed as a political question.