Your comment is pertinent, so I won't change mine. Apologies.

In my country the word is frequently used to carry sarcasm towards the role that Lukashenko believes himself to have. In other words, it is meant as sarcasm towards the tyrant's ego, not the gullibility of the nation.

i think you are mistaken here. Bat'ka in this context is more like Bat'ka Mahno, ie. a leader outside of formal rules and leading more by personal power like a leader of a gang or a rebellion (or for example in Belarussian context - "Bat'ka Minay", a commander in WWII Belarussian guerilla resistance https://ru.wikipedia.org/wiki/%D0%A8%D0%BC%D1%8B%D1%80%D1%91...).

> it was originally used to mock Belarusian for supposedly liking his approach to ruling the country.

not even close. It has always been used in the "leader" meaning described above.

>He's no father to any of us, and it's insulting to Belarusians to see someone referring to him this way.

as nobody uses it as "father" in this context it is hard to see your point.