I think you've summarized a lot of truths with this. Also, in my own experience a lot of people will say, "I'm not judging" because they want more information for the personal satisfaction of hearing more about what they feel is a controversial or judgment-worthy. So "I'm not judging" is often a reliable clue that someone is.
From what I've noticed, "I'm not judging" came into common usage in the recent era of political correctness. People who really aren't judging shouldn't have to say anything at all. There are a million other ways to demonstrate by expression or body language that a person is open and objective. I'll tell people I don't judge if I'm having a conversation about judgment. Otherwise, I normally just assume people who know me are aware that I try very hard not to engage in the practice. I don't feel any compulsion to announce it.
How true.
I always thought Jerry Seinfeld made that dynamic famous when he said, "Not that there's anything wrong with that!"