Lets consider both horns of this dilemma. We are to love our enemies and turn the other cheek. This refers to our actions acting as individuals. However, scripture also addresses actions taken by the "church" to protect the gospel from false teachers. The difference is we would be acting in concert with other believers, and our weapons are words, speaking out against the destructive heresies. And finally, scripture allows believers, acting under the color of government authority to use violence. So there is no dilemma once we acquire a well studied understanding of all the related passages. Several of the "saints" mentioned in
Hebrews 11 were "mighty in war."
1. If we love our enemies and turn the other cheek as individuals as you say, as Jesus taught, then when are we NOT to act as an individual?
2. Church actions against false teachers, as you mention above, are to be addressed, but not with violence. I think you handled that well.
3. I do not know any passage in the New Testament or Old that would support using violence "under color of government authority." Let me add "secular" government authority. Israel as God's chosen people, was not a secular nation, and it was led by prophets and priests through whom God spoke. God very explicitly mandated and directed the specifics of battles of the OT "saints." I am unaware of that happening in any military or other violence today. If any person on earth told me that God had directed him to have me commit violence, I would be very skeptical indeed, inquire into the persona walk with God, and then make an individual choice on the matter. If God clearly does for me what He did for the "saints" and directs me to commit violence, then, I would do so. I have never known such a case in my life.
I don't think the dilemma is very difficult unless we are determined and prepared to take up violence no matter what Jesus taught. I know we can invent gray areas, and I could name a few where I have been involved, but overall, I think that if we prepare to avoid violence, we will find that most of us will seldom if ever encounter it.
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Note: Violence/non-resistance exception--Once I took some children to the zoo. A young man with mental health issues suddenly decided to harm other children and then proceeded to climb into a wolf pit. He was a very large, strong, young man. I happened to have some martial arts skills acquired in my misspent youth, and used some force to subdue the young man until help arrived. No serious violence was used and I think that everyone including the young man (later) agreed restraint was in the best interest of everyone and an act of kindness. I did not use a gun or pain, although I did use some force. Was that wrong?
May God give us wisdom in such cases and in that case, I think He did. My heart is entirely open to Biblical wisdom on the matter.