Earlier quoted context omitted.
The "invisible hand" metaphor used by Adam Smith is not an explanatory mechanism , and if anything is an admission that the specific mechanism isn't understood . In use at the time and earlier, it had the sense of "the invisible hand of Providence" (or God). Though Smith, as Hume, was almost certainly what we'd now call an athiest. He used the term three times, in three different books: The Theory of Moral Sentiments…
Also, Adam Smith's example of the invisible hand was as a mechanism to prevent so-called free trade, and raise protectionist tariffs. The people you mentioned have twisted Smith's words into the exact opposite meaning - they say Smith's invisible hand sweeps away protectionist tariffs and allows international free trade. He said the complete opposite of what they say he said.
Smith compared free(er) trade to Mercantilism - extremely un-free, Royal patent oriented rent seeking .