In the purest form, I suppose they are saying that you do not understand the extraneous circumstances for their actions. In other words, do not hold me accountable for my actions, or my hypocrisy, because I have a good excuse.
In a way, asking not to be judged is a defense mechanism. It is a process where the criticism is actually placed back on the judger. It is a process where rather than perhaps explaining one's actions, the judged replies that they are offended by the criticism--in other words, shame on you for holding me accountable. Thus rather than offering an excuse or explanation, the question is what gives someone the right to note the inconsistency . . . essentially saying, "I'm going to do whatever I want and it's none of your business to note otherwise."
What I think people are really saying is not "don't judge me," as so much as they are saying don't "criticize me." It's not the actual judging process that bothers people--it is the conclusions drawn. For example, do people complain when a judgment leads to a positive comment? If I said to someone "You are really doing great a thing volunteering at the food bank," would anyone ever respond, "Hey don't judge me!"?
Either way, and regardless as to why people ask not to be judged, it is a pointless request. In fact, I think the mere request only increases the judging.
The reality is that we are all "judged" (and we can debate what that really means) all the time whether we like it or not. We are judged by the way we look--whether we are in shape or overweight, or whether we have piercings or tattoos. We are judged by the kind of car we drive, the food we eat, the house we live in, the way we talk, our political affiliation and who are friends are. The list of things for which we are judged goes on for pages. It is pointless to attempt to live a "judged-free" life. It happens instantly, all the time, consciously or subconsciously.
And, whether we admit it or not, we all do our fair share of judging--that is, forming an opinion about people based on stereotypes, associations or previous knowledge about the individual. We do it quickly and often unfairly. Consider the differences in type of car and bumper sticker--the first a Toyota Prius, with "Obama" and "Coexist" bumper stickers on it, the second a Hummer with "gut buck" and "Honk for Jesus" bumper stickers. In just that description, and without even seeing the drivers, we've probably already formed an opinion regarding his or her values and morals.
I suppose as a columnist who focuses on social criticism, I do more than my fair share of judging. While I certainly have engaged in a life philosophy, the brunt of my criticism falls upon those who are "inconsistent" in their life philosophy. Individually, and in person, I think people are much more reasonable than their views--compromise is surprisingly easy at times. However, I think there is often a disconnect between people's life philosophy and the way they live their lives. In this way, I often have more respect for fanatics--those with whom I might disagree, but live in accordance with their beliefs. I have a much greater difficulty with those whose philosophy changes with their self-interest-people who do not stand for anything other than what benefits them the most. While we all stray from time to time, I believe in a "principled life."
I think living a principled life means never having to worry about "being judged." Criticism largely comes from inconsistency and hypocrisy. If one lives according to his or her principles, then there is a simple explanation--based on our personal values and morals, for which there should be no apology.