Who am I kidding? When confronted with truth and facts, liberals just stick their fingers in their ears and shout, "I cAn'T hEaR yOu! I cAn'T hEaR yOu!"
To start with, the passage which all you shallow liberals typically point to compares the sin in a person's life as wood, either a log or a plank, vs. a splinter. For those who should know better, even their "smaller" sins are much more egregious, because they have knowledge and awareness (allegedly) that the person they are judging does not have. Sin is sin, but God knows when a person is doing so in ignorance (ignorance of the Law is still no excuse). Compare Psalm 19 ( https://www.biblegateway.com/passage/?search=Psalm+19%3A12-13&version=ESV )
So in Matthew 7, where we see Jesus stating, "“Judge not, that you be not judged.", He goes on to say, "For with the judgment you pronounce you will be judged, and with the measure you use it will be measured to you." A repentant sinner has no problem being rightly judged, and in fact wants it, as is further seen in that Psalm 19 passage.
But Jesus goes on to explain that those He was speaking to, the religious leaders of that day, and complete hypocrites, that they should first deal with their own sin ("first remove the log from your own eye"), and then goes on to say, " . . . and then you will see clearly to take the speck out of your brother's eye." Even for an unbeliever, without the aid of the Holy Spirit, should be able to follow the progression of what Jesus was actually saying.
Elsewhere in the Bible, we see this:
Let a righteous man strike me—it is a kindness;
let him rebuke me—it is oil for my head;
let my head not refuse it.
- Psalm 141:5
So, if THAT is the attitude of the person who is making right judgments about another, this is precisely the approach we are to take. A nonbeliever can apply some of this, but generally speaking, they haven't the faculties to do so accurately, having rejected the standard of God needed to make right judgments.
And if that isn't clear enough for you, there's this, emphasis added:
1 Corinthians 2:14-16
The natural person does not accept the things of the Spirit of God, for they are folly to him,
and he is not able to understand them because they are spiritually discerned.
THE SPIRITUAL PERSON JUDGES ALL THINGS,
but is himself to be judged by no one.
“For who has understood the mind of the Lord so as to instruct Him?”
But we have the mind of Christ.