I think it's a riff on an old meme I don't quite remember. But the idea is like,

• people are doing an innocuous thing
• something declares that they thus must hate dubiously related thing

Like, someone playing checkers. Someone says "oh you're playing checkers because you hate chess!?". You can kind of see how they made that leap through several errors (view chess and checkers as mutually exclusive opposites)

So the person in the quote thinks banning whoever is a non sequitur, I guess.