Wow! Your question is thought-provoking!
Let's dissect Matthew 7:1-2 to first discover what the gospel writer is really talking about.
"Do not judge, or you too will be judged. For in the same way you judge others, you will be judged, and with the measure you use, it will be measured to you."
In this passage Jesus condemns the habit of criticizing others while ignoring one's own faults and shortcomings. Believers must first submit themselves to God's righteous standard before attempting to examine and influence the conduct of other Christians. In addition, judging others in an unjust manner also includes condemning a wrongdoer without desiring to see the offender return to God and His ways.
On the other hand, this passage must not be used as an excuse for laxity in exercising church discipline. Jesus is not taking away from the necessity of exercising certain degrees of discernment or of making value judgments with respect to sin in others. Elsewhere in the New Testament (Matthew 7:15, John 7:24, 1 Corinthians 5:12, Galatians 1:9, 1 Timothy 4:1, etc.) we are commanded to identify false ministers within the church and to evaluate the character of individuals.
Now back to your question. How can Christians then serve on juries? Human government is an institution set up by God for many reasons, including the function of properly judging and protecting the masses and individuals from those who practice wrongdoing.
Let's go to Exodus 18 and learn the principle that God taught Moses through his father-in-law, Jethro. Because of man's inherent sinful condition, there always have been wrongdoers and law breakers. God knew that, and instituted a way to properly judge these individuals, thus giving them due recompense.
In Exodus 18:13-22 we read:
"The next day Moses took his seat to serve as judge for the people, and they stood around him from morning till evening. When his father-in-law saw all that Moses was doing for the people, he said, 'What is this you are doing for the people? Why do you alone sit as judge, while all these people stand around you from morning till evening?' Moses answered him, 'Because the people come to me to seek God's will. Whenever they have a dispute, it is brought to me, and I decide between the parties and inform them of God's decrees and laws.' Moses' father-in-law replied, 'What you are doing is not good. You and these people who come to you will only wear yourselves out. The work is too heavy for you; you cannot handle it alone. Listen now to me and I will give you some advice, and may God be with you. You must be the peoples' representative before God and bring their disputes to Him. Teach them the decrees and laws, and show them the way to live and the duties they are to perform. But select capable men from all the people--men who fear God, trustworthy men who hate dishonest gain--and appoint them as officials...Have them serve as judges for the people at all times..."
God in His wisdom established government as a means of properly controlling, organizing, unifying, and implementing sound judgment. Of course, anything man touches, he usually corrupts, abuses or misuses. This is certainly true with governments at large. However, wrongdoing in this life must be judged in a calculated fashion. Therefore, God has made a way through judges to carry out this necessity. In our democratic system, juries are selected to carry out sound judgment, although in cases like the Casey Anthony trial, we rightfully wonder about our system's loopholes!
In Matthew 7:1-2, Jesus uses the word judge to refer to undo criticism of another individual when we ourselves have similar or even greater issues at hand.
"Why do you look at the speck of sawdust in your brother's eye and pay no attention to the plank in your own eye? (verse 4).
Thank you for your excellent question.
