The other exorcist
Whether one outside the company may act in Christ's name, and what that says of the church's bounds.
Mark 9:38-41
38John said to him, “Teacher, we saw someone who doesn’t follow us casting out demons in your name; and we forbade him, because he doesn’t follow us.”
39But Jesus said, “Don’t forbid him, for there is no one who will do a mighty work in my name, and be able quickly to speak evil of me.
40For whoever is not against us is on our side.
41For whoever will give you a cup of water to drink in my name, because you are Christ’s, most certainly I tell you, he will in no way lose his reward.
What each tradition says
Rabbinic / Midrashic
The Jewish Encyclopedia notes that Jacob of Sekanya desired to cure, in the name of Jesus, one who had been bitten by a snake. R. Ishmael, however, would not permit it, preferring rather to let his sister's son die.
Kaufmann Kohler, Ludwig Blau, Exorcism (Jewish Encyclopedia, 1901-1906) — 'Jewish Christianity' — Jacob of Sekanya and R. Ishmael
Patristic
The Apostolic Constitutions state that an exorcist is not ordained, for it is a trial of voluntary goodness and of the grace of God through Christ by the inspiration of the Holy Spirit. One who has received the gift of healing is declared by revelation from God, the grace in him being manifest to all.
The Apostolic Constitutions (Constitutions of the Holy Apostles), Constitutions of the Holy Apostles, Book VIII, § 26 ('The Same Apostle Concerning the Exorcist') (ANF vol. 7, ed. Roberts & Donaldson) — Book VIII, § 26, 'Concerning the Exorcist'
Catholic
Patrick Toner argues it does not seem reasonable to take this reply as mere irony or as an argumentum ad hominem that implies no admission of the fact. He notes that elsewhere Mark 9:37-38 records a non-disciple casting out demons in Christ's name, and Christ refused to reprehend or forbid his action.
Patrick Toner, Exorcism, in The Catholic Encyclopedia, vol. 5 (1909), served at newadvent.org — 'Exorcism in the New Testament' — on Mark 9:37-38 (the non-disciple exorcist)
Orthodox
No sourced position found. Checked the Eastern fathers in the ANF/NPNF volumes on hand (Chrysostom's homilies on Matthew, Acts, Romans, 1-2 Corinthians, John and Hebrews; Cyril of Jerusalem's Catecheses; Athanasius; the Seven Ecumenical Councils) for comments on Mark 9:38-40 / Luke 9:49-50 ('forbid him not', 'not against us'): Chrysostom wrote no homilies on Mark, no PD English Eastern exposition of the passage was found, and Philaret's Longer Catechism (pravoslavieto.com) has no comment. (The Apostolic Constitutions' constitution on the exorcist is the patristic row above.)
Reformed / Protestant
Calvin thinks the man may have embraced Christ’s doctrine and acted with no bad intention, but since Christ gave this power only to chosen heralds, he rashly seized the office. Though wrong to imitate the disciples without a command, his boldness succeeded because the Lord was pleased to bring luster to his name.
John Calvin, Commentary on Matthew, Mark, Luke, vol. 2 (trans. William Pringle; Calvin Translation Society) — Commentary on Mark 9:38 ('we saw one casting out devils in thy name')
Evangelical
John answered as if asking whether they should receive one not following them. They saw a man casting out devils in Jesus' name, probably a disciple of John the Baptist who believed in Jesus but did not yet associate with the Lord's disciples. They forbade him because he did not follow them; Wesley notes this temper is often in us.
John Wesley, Explanatory Notes upon the New Testament — Notes on Mark 9:38 ('And John answered him')