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Many Christians fall all over themselves about the issue of judging people. Jesus said we're not to do it. Many people who call themselves Christians think it's their duty to point out when someone is involved in sin.
There's more than one meaning for 'judge.' There's 'passing judgment and sentencing someone,' and there's 'forming an opinion,' judgment. The latter is natural and mostly unavoidable; it's the meaning most of the people who think it's okay to judge mean when they say 'it's okay to judge.' Like when you judge a book after reading only the title.
Passing judgment and bringing a charge against a person is what Jesus was trying to get Israel to discontinue. They were Johnny-on-the-spot for doing that (see John 8).
Here's an example to consider: you have a friend and she's cheating on her husband. You go to her and tell her it's wrong and she needs to stop. You're not judging her, you're telling her your opinion about what she's doing, and we all know that infidelity is wrong. Your opinion is aligned with truth.
If you go and tell her husband you'd be going from being a friend to being a judge. You would be handing out consequences; judges do that; they pass sentences on transgressors. A friend would try to restore her (get her to stop). Judges don't try to restore defendants; they look at evidence and decide guilt, innocence, and consequences.
That's what Jesus was trying to get them to stop doing. Judges don't correct people; they issue rulings.