Reading the Book of Mishlei, I surprisingly stumbled upon an apparent answer to my question.
In Mishlei 9:7 we read:
He who chastens a scorner takes disgrace for himself, and he who
reproves a wicked man, that is his blemish.
and he who reproves a wicked man, that is his blemish: It is a blemish to the one who reproves [him], for this one berates him and
does not heed him. This is a warning that it is forbidden to talk with
those who entice to worship idols, even to reprove them and to draw
King Solomon and Rashi basically say it's a waste of time and nerves to convince Christians and other idolaters to abandon idolatry. They will still cling to their stupidity and hate you for showing them how stupid they are (my experience confirms the proverb is true).