Can Christians be judges? Yes we are called to be judges, but not according to the law.
Romans 2:1 NKJV
Therefore you are inexcusable, O man, whoever you are who judge, for in whatever you judge another you condemn yourself; for you who judge practice the same things.
What then are we to judge?
15 “Beware of false prophets, who come to you in sheep’s clothing, but inwardly they are ravenous wolves. 16 You will know them by their fruits. Do men gather grapes from thornbushes or figs from thistles? 17 Even so, every good tree bears good fruit, but a bad tree bears bad fruit. 18 A good tree cannot bear bad fruit, nor can a bad tree bear good fruit. 19 Every tree that does not bear good fruit is cut down and thrown into the fire. 20 Therefore by their fruits you will know them.
Why we are to judge that is for another question.
If so: can they ever sentence someone to death? Yes.
Acts 5:1-11 NIV
Now a man named Ananias, together with his wife Sapphira, also sold a piece of property. 2 With his wife’s full knowledge he kept back part of the money for himself, but brought the rest and put it at the apostles’ feet.
3 Then Peter said, “Ananias, how is it that Satan has so filled your heart that you have lied to the Holy Spirit and have kept for yourself some of the money you received for the land? 4 Didn’t it belong to you before it was sold? And after it was sold, wasn’t the money at your disposal? What made you think of doing such a thing? You have not lied just to human beings but to God.”
5 When Ananias heard this, he fell down and died. And great fear seized all who heard what had happened. 6 Then some young men came forward, wrapped up his body, and carried him out and buried him.
7 About three hours later his wife came in, not knowing what had happened. 8 Peter asked her, “Tell me, is this the price you and Ananias got for the land?”
“Yes,” she said, “that is the price.”
9 Peter said to her, “How could you conspire to test the Spirit of the Lord? Listen! The feet of the men who buried your husband are at the door, and they will carry you out also.”
10 At that moment she fell down at his feet and died. Then the young men came in and, finding her dead, carried her out and buried her beside her husband. 11 Great fear seized the whole church and all who heard about these events.
If not: can't they judge in any matter, or are they allowed to settle domestic disputes or rule in material matters? We where called to settle domestic disputes and rule in material matters.
1 Corinthians 6:1-8 NKJV
Dare any of you, having a matter against another, go to law before the unrighteous, and not before the saints? 2 Do you not know that the saints will judge the world? And if the world will be judged by you, are you unworthy to judge the smallest matters? 3 Do you not know that we shall judge angels? How much more, things that pertain to this life? 4 If then you have judgments concerning things pertaining to this life, do you appoint those who are least esteemed by the church to judge? 5 I say this to your shame. Is it so, that there is not a wise man among you, not even one, who will be able to judge between his brethren? 6 But brother goes to law against brother, and that before unbelievers!
7 Now therefore, it is already an utter failure for you that you go to law against one another. Why do you not rather accept wrong? Why do you not rather let yourselves be cheated? 8 No, you yourselves do wrong and cheat, and you do these things to your brethren!
Is sentencing or being on a jury a sin? No.
1 Corinthians 5:1-5 NKJV
It is actually reported that there is sexual immorality among you, and such sexual immorality as is not even named among the Gentiles—that a man has his father’s wife! 2 And you are puffed up, and have not rather mourned, that he who has done this deed might be taken away from among you. 3 For I indeed, as absent in body but present in spirit, have already judged (as though I were present) him who has so done this deed. 4 In the name of our Lord Jesus Christ, when you are gathered together, along with my spirit, with the power of our Lord Jesus Christ, 5 deliver such a one to Satan for the destruction of the flesh, that his spirit may be saved in the day of the Lord Jesus.
1 Timothy 1:20 NKJV
of whom are Hymenaeus and Alexander, whom I delivered to Satan that they may learn not to blaspheme.