It is ironically interesting to note that those who love to consider themselves non-judgmental are in need of the verse in Matthew 7.
For these actually have put themselves in a position where they are like an outside observers, having no involvement in the goings of the world, making them "not as sinful or responsible" as the average human beings.
So "Judge not, that ye be not judged...", and they are stuck here with their ignorance and shallowmindedness. For they cannot realize it is a God given nature to judge. So instead of realizing how much improvement they have to make on themselves to not be a hypocrite or living in their "I am alien observing the human race" fantasy, instead of realizing the next few verses' connection to the first, they HAVE TO misinterpret it as "not applying to themselves for they are not involved", but applying to those who bring wars and conflicts.
One of the threat of judging others is to become nonchalant, indifferent to self-reflection.