This is a popular verse to quote. But it's also popular for "Conservative" Christians to insist that "Liberal" Christians are taking this verse out of context when they quote it with the intent of saying Judgmentalness is inherently Un-Christian.
They say the point Jesus goes on to make is that you need to make sure your not guilty yourself of the Sin your Judging someone for before you judge them.
No, the point of everything Jesus goes on to say is like all the verses where he talks about the importance of not sinning with the intent of showing we can't be saved by our own Righteousness. Read Romans 1-3.
In John 8, when Jesus said "Let he among you who is without Sin cast the first stone". There is no qualifier of not guilty of the same sin. Paul said we are all Sinners.
"But, when your Saved you won't be or at least shouldn't be sinning like you did before". Again Romans 1-3 Paul is specifically telling those believers they're in error for judging the non believers.
We are supposed to be informing the World that we're all condemned because we're all imperfect. But Jesus died to take the penalty of Sin for us.
Judgment is for Jesus alone.