I find people who play this "do not judge" card are usually in one of two categories:
1. They want to do what they want without consequence
2. They do not want anyone to tell them they are wrong.
Truth is... There are MANY things we are judged for throughout life by others whether we like it or not. For me the Lord is saying do not judge wrongfully or with malice, because if you judge in this manner you will be judged in like manner. However we have to make judgment calls, were it not so... Strange people could enter our homes, Bishops would give temple recommends to anyone who just answers right, policemen would not inspect a suspicious person, etc.
From the context, it is clear that when the Savior said that we should not judge unrighteously, what He meant was that we should not find fault with others for doing the same things that we do. In other words, we should not be hypocrites. If there was one thing that the Savior frowned upon it was hypocrisy. A good example: one time I saw someone driving out of the parking lot at work without stopping at the stop sign, and I judge them. But then, when I left work to go home, what did I do? The exact same thing--I failed to stop at the stop sign. How can I expect to be judged?