The Christian duty to be judgmental
Recognizing God's grace and mercy does not mean we cannot judge violent predators and protect society from them by locking them up or executing them.
Should Christians judge? Absolutely yes. Not only is there no commandment not to judge, but we are commanded to judge. The most common retort to that duty is Matthew 7:1, but verse 5 is the context: Not to judge as a hypocrite. We remove the log from our eye so we can remove the speck from our brother's eye. Matthew 7:6 tells us not to give holy things to dogs, and we cannot obey that unless we judge who the dogs are.
We are to be like Jesus, right? Jesus pronounces thunderous judgment against Chorazin, Bethsaida and Capernaum in Luke 10. Jesus tells us in John 7:24 to "Judge not according to the appearance, but judge righteous judgment." The early church followed Jesus' example. In Acts 5, the Holy Spirit strikes down Ananias and Sapphira for lying about the price of the land they sold, even though they had a right to keep what they wanted of the sale price. This is after the Apostle Peter judges them for lying. The Holy Spirit and Jesus are one.
What about the Gospel? Yes, Christians should be forgiving, and we should recognize that the grace of God is available to everyone. If Ted Bundy and Jeffrey Dahmer genuinely repented and turned to Christ, they are both in Heaven communing with Jesus Christ despite their crimes of rape, murder and cannibalism. Wicked King Manasseh of Judah burned his own infant children to death, but was forgiven. He is even in the line of Jesus Christ. Praise God for His mercy to even the worst sinners!
However, recognizing God's grace and mercy does not mean we cannot judge violent predators and protect society from them by locking them up or executing them. Protecting the innocent is literally the entire purpose of having a criminal justice system and is the primary duty of government. The Apostle Paul writes in Romans 13 that the governing authorities do not bear the sword in vain. If it is "sinful" to judge, then no Christian could ever serve as a judge or in any other capacity that requires them to practice judgment - including as a financial auditor to make sure money is spent according to the law or company policy.
Judgment is unavoidable. We judge every single day in little ways. We judge other drivers for our own safety when we decline to take our right of way because we (correctly!) realize they will break traffic rules and do something dangerous. Parents judge other children and families for the protection of their children. Many wise fathers and mothers have told daughters and sons not to date or marry a specific person. They want to protect their children from abuse and heartbreak. How can that be sinful?
We have to get beyond the meme that judging is bad. Judgment can be bad, sure, if done self-righteously or with bad motives. Judgment is certainly bad when you assume things wrongly and level false accusations against people. Judgment is wicked when you repeat lies about people. But the improper use of a thing does not invalidate its proper use. The fact that judgment can be misused does not mean judgment itself is bad. Forgiveness is real, grace and mercy are available, but those three are meaningless without judgment of sin. Judgment is good and necessary.