Ah, there's a reason for your misunderstanding about biblical judgment.
A refresher:
"You hypocrite, first take the log out of your own eye, and then you will see clearly to take the speck out of your brother's eye" (Matthew 7.1-5 ESV)
Let's look at the scriptural foundation for correcting others:
John 8
9 At this, those who heard began to go away one at a time, the older ones first, until only Jesus was left, with the woman still standing there. 10 Jesus straightened up and asked her, “Woman, where are they? Has no one condemned you?”
11 “No one, sir,” she said. “Then neither do I condemn you,” Jesus declared. “Go now and leave your life of sin.”
In the case of this nonbeliever, Jesus doesn't pronounce sentance on her and so models for us what it means to not commit the Biblical sin of judging their neighbor. He does make a judgement about her character and tells her to straighten up.
Matthew 4:17 "From that time on Jesus began to preach, "Repent, for the kingdom of heaven is near.""
He had to tell people that they were sinners if he was going to tell them they were supposed to repent of something. What would you say to Jesus if he told you that you needed to clean up your act?" Would you tell him to stop judging you?
Matthew 23:
16“Woe to you, blind guides! You say, ‘If anyone swears by the temple, it means nothing; but if anyone swears by the gold of the temple, he is bound by his oath.’</SPAN>
17You blind fools! Which is greater: the gold, or the temple that makes the gold sacred?</SPAN>
18You also say, ‘If anyone swears by the altar, it means nothing; but if anyone swears by the gift on it, he is bound by his oath.’</SPAN>
19You blind men! Which is greater: the gift, or the altar that makes the gift sacred?</SPAN>
20Therefore, he who swears by the altar swears by it and by everything on it.</SPAN>
21And he who swears by the temple swears by it and by the one who dwells in it.</SPAN>
22And he who swears by heaven swears by God’s throne and by the one who sits on it.</SPAN>
Here's Jesus chastising people who are righteous by their own standards as opposed to God's and leading others to adhere to what he taught were false methods of attaining righteousness.
The Great Commission
Matthew ch. 28
16 Then the eleven disciples went to Galilee, to the mountain where Jesus had told them to go.
17 When they saw him, they worshiped him; but some doubted.
18 Then Jesus came to them and said, “All authority in heaven and on earth has been given to me.
19 Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit,
20 and teaching them to obey everything I have commanded you. And surely I am with you always, to the very end of the age.”
He says to go and tell people all over the world that they are sinners and need to repent when he talks about making disciples of all nations. He tells them to teach the entire world about areas of their lives that need correction. In other words Jesus is commanding his disciples to model their ministries after his. Is Jesus actually commanding his disciples to be judgemental or could it be that your definition of what constitutes judgementalism is not the Biblical definition? My point is that if you have a problem with Christians saying that things what some people believe in or do are evil then you have a problem with what Christ has commanded his followers to do. Again, nobody is proposing that we hand down a sentance for your sins as that IS judging. Face it, only the enemy of our souls creates false doctrines in which it's sinful to correct others.