This term evolved into the modern "idiot" which we are familiar with.
After the extermination of Melos they could credibly say they were less responsible for the actions of the polis.
And had a higher chance of deflecting the inevitable revenge on to the non idiotes Athenians.
For one thing, wouldn’t everyone claim they were against their old polis? How would the invaders have any idea who was an idiote?
I just don’t believe it’s at all easy to avoid the fate of your nation , and I especially doubt that the politically ignorant have a better chance of avoiding that fate than the well informed.
The counter extermination was only 5% of Athens total population, or so historians say, so it seems like a lot of nuance was shown.
That fact alone doesn't demonstrate nuance. It's possible that 5% of the population was innocent and treated as scapegoats, or chosen randomly, or that anyone high profile regardless of guilt was chosen to die.
Unless there's data on who was actually innocent or guilty, the mere fact that extermination was selective doesn't mean it was in any way accurate.
Of course nobody can prove either way beyond a reasonable doubt for something that happened so long ago.
Taking parent's cue of assuming lack of agency - you can even replace "politics" with "the weather", and gp's comment still makes sense, parents inverted riposte does not make sense under its own priors. We can't change the weather, but it's prudent to know which days to carry an umbrella.
My interpretation of the statement is that you can't ignore forces that affect you, even if they bore you. However loudly or frequently you declare or think "I don't care for gravity" matters not as it exists outside of your awareness or acknowledgement of it.