I would lie, cheat, and steal, murder and rape, if I knew nobody
would judge me, including myself. Would I be active in volunteering if I didn't feel the need to judge myself a good person? Would I try so hard to be honest? Another way to put it, anonymity (when judgments cannot be traced to an individual) has costs, as the high numbers of "trolls" and flaming comments on the internet show.
Even as we discuss not judging, we are making judgments, at the very least judging what a reaction would be, down to explicit judgments of others such as "far worse than.." or "bigger problems than..." Judging is inherent in human nature, it's a response based on prior experience ("Fool me once, shame on you, fool me twice, shame on me"). For instance, stereotypes are concentrated judgments based on perceived social experience, which is why it's so hard to break them: they are assumed to be statistically high, so you need a lot of quantity or a few high quality cases to override them.
I found the book Predictably Irrational
by Dan Ariely to be very interesting and pertinent to this discussion. He empirically tests that almost everyone cheats given the opportunity, but we only cheat a little bit before our internal judgment mechanisms kick in. "The true measure of a person's character is what he or she will do when they know they won't be caught" is another flavor of this question, in my opinion. I think we all like to think of ourselves as honest and good, and based on these findings, for the most part, most people are, but I think Ariely's findings are right that we will cheat a little if we know we won't be caught (or judged). For example, would you really fight to get back to the counter of a crowded store if you got extra change? As an aside, his treatment of the high cost of free is also very thought provoking in light of Eden's point and review system.
I think only the completely ignorant or thoughtless can be truly "non-judgmental." We are always making judgments, whether or not we express them, and being accepting is simply judging a person's worth based on their biological status as a human being or some other universal status above their identification with a particular group that may not be in favor with others. You can love a thief but you probably should not trust them with your car, which is a form of judgment. I try to be accepting of others but being non-judgmental is a false goal.
Of course, this may be simply my personal definition of each of the terms. Let me know what you all think, I hope I didn't cram too much into one post.