Those who cry against being judgmental are not moved by the Holy Ghost. The scriptures plainly teach:
Moroni 7:15 For behold, my brethren, it is given unto you to judge, that ye may know good from evil; and the way to judge is as plain, that ye may know with a perfect knowledge, as the daylight is from the dark night.
The JST of Matt 7 makes clear the Savior's meaning, changing the phrase "Judge not lest ye be judged" to "Judge not unrighteously, lest ye be judged. But judge righteous judgement."
I have no idea how it is possible that we have been so unwilling to actually believe this plain scripture. Christ, himself, personally gave the command to judge righteous judgement. Moroni 7 explains in all detail what that means. It means to call evil evil and to call good good. It means to judge by the light of Christ, rather than by any other method.
Now, it is true that we should overlook one another's petty faults. That is a critical part of the gospel. And, rather unfortunately, we have inherited the phrase "judge not" as a phrase that is sometimes used to mean exactly that.
But those who cry against judgement are not those who are concerned with passing over petty faults. In fact, not uncommonly they are like wolves to the prey when they think someone else is being "judgmental". They do not judge righteous judgement. They do not call evil evil. In fact, they are angered by statements that plainly call evil evil. And consequently, they not only insist that evil needs to be called good, they end up forcefully calling good evil as well.
It was Christ who said
Matthew 23:23 Woe unto you, scribes and Pharisees, hypocrites! for ye pay tithe of mint and anise and cummin, and have omitted the weightier matters of the law, judgment, mercy, and faith: these ought ye to have done, and not to leave the other undone.
If those who cried out against judgment were moved by the Holy Ghost, they would call good good without hesitation. They would call evil evil without guilt or remorse. They would search diligently in the light of Christ to know good from evil.
You cannot reject knowing good from evil by the light of Christ, and yet still be following the Holy Ghost.