Judging is to regard a person as a wrongdoer deserving of disapproval and condemnation and retribution.

Christians seem to define non-judgmental as meaning that you wait for the sinner to repent and forgive when they do.  Just as to hate reproductive rights is to hate women especially the vulnerable women who need them, so this loving the sinner and hating the sin is not love but a passive aggressive pretence.
Some Christians lie that Jesus condemned judging. He did not. He only said that before you judge make sure you are not worse than the person you judge. He said you may see the speck in the eye of another and ignore the plank in your own. He said get rid of the plank and then judge. 
Christians say he forbade hypocritical judgement in saying all that. He actually forbade unfair judgement. It is not fair to judge somebody who is not as bad as you.
Other Christians say we must judge the sin and not the sinner. This makes absolutely no sense at all. It only makes a hypocrite of the person who claims to believe it.
Those who when their actions are condemned say, "You have no right to tell me what I am doing is wrong - judge not that you be not judged." They are hypocrites who judge those who judge them. They are being judgemental though they condemn being judgemental!
To judge that there is a God who will judge those who judge you is indirectly judging them.
You insinuate that God will judge those who judge you! So you admit that judging is not necessarily sinful! You want people to believe that judging need not be sinful and is necessary. So you are humbly saying it is only sinful when you are being judged!
The Catholics say you must tell those who have sex outside marriage for example that they are doing a great wrong and that sex outside marriage is a sin that merits everlasting torment in Hell from the moment of death. They deny that saying this means they are judging the persons as going to Hell. There could be weakness or ignorance that prevents them from deliberately committing a great evil. Their responsibility might be mitigated. Also they might soon repent and escape Hell so you cannot say they are already condemned to Hell. You cannot judge them that way. The Church says it can judge that somebody is doing wrong but they cannot judge the person's exact intentions. For example, murder is a mortal sin but if the murderer was given drugs against his will it would mean he was not being fully himself and so did not intend to commit a mortal sin.
Matthew 18 records that Jesus said that those who continue in sin after being told they are sinners must be shunned.
Should the true Christian be constantly disapproving? Even if you say you cannot judge a person as bad or how bad they are because you cannot know all about them, then you are disapproving in the sense that, "They might be terrible inside. They might not." That is light judgement not non-judgement. Non-judgementalism is often a cover for hypocrisy.
Even believers do not put God first very much, it follows that the Christian must always have a problem with everybody.

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