This verse is constantly taken out of context.
Contextually, God’s word is clearly talking about self-righteous judgment.
Luke 6:39 - 42 makes that clear.
39 And He spoke a parable to them: “Can the blind lead the blind? Will they not both fall into the ditch?
40 A disciple is not above his teacher, but everyone who is perfectly trained will be like his teacher.
41 And why do you look at the speck in your brother’s eye, but do not perceive the plank in your own eye?
42 Or how can you say to your brother, ‘Brother, let me remove the speck that is in your eye,’ when you yourself do not see the plank that is in your own eye? Hypocrite! First remove the plank from your own eye, and then you will see clearly to remove the speck that is in your brother’s eye.
Christians must judge but not do so hypocritically. Of course the ultimate judgment belongs to God.
Thank you for summing it up nicely.