
I have discovered that, apparently, a pat on the head and smiling at them before walking away is not considered polite.

I have discovered that, apparently, a pat on the head and smiling at them before walking away is not considered polite.
There is no polite way to disabuse them of their ill-considered notions.
Politesse is not effective – blunt force trauma to their worldview is the only reasonable measure.
I suppose that if the interlocutor is deemed to be possibly salvageable, giving them a copy of Economics in One Lesson might be worth a try Giving them a copy of The Virtue of Selfishness is probably only useful as a second step.
Kurt