You are correct in your observation that Christians are not given any kind of special 'card blanche' permission to murder, or even fight in national wars etc.
Too much is often made of the fact that on one occasion, John the Baptist told (Roman?) soldiers simply to 'be satisfied with your wages'. Many have claimed that this means both JB and JC approved of the occupation of 'soldier' or at least 'policeman', and even 'military occupier'.
But this is untenable. For Roman soldiers were not at liberty to 'volunteer' for service, or 'retire' from the army at will, or even quit their jobs like a modern policeman. The penalty for desertion in almost every army (especially during wars or battles) has always been torture and execution, usually in a horrible or brutal manner.
(Even in the British Navy, men were routinely keelhauled or horsewhipped for minor infractions of discipline or 'backsass'.)
Had John the Baptist said, "Just quite your post, and pick flowers with us here by the Jordan." he would have been sentencing them all, including innocent Jewish/Christian followers, to an immediate and instant slaughter.
John was probably speaking in recognition of the severe and inescapable conditions they were all under because of Roman 'martial law' during the occupation.
Secondly, Jesus told His followers to obey the Law, (Torah), not enforce it, or impose it upon others. Just looking after the log in your own eye is a full-time occupation in God's eyes. Its enough to follow the Spirit of the Law yourself, and speak the truth when asked.
Running around arresting people and locking them up for 'breaking the Law' was exactly what Paul did BEFORE he was saved, and exactly what he STOPPED doing, after he came to know the Lord.
It is true that Paul continued to 'discipline his flock, and followers', but this appears to have been limited to casting out unrepentant, stubborn, or arrogant, or deceivers and fakes out of the Church.
Christians did not 'stone to death' members of their congregations who broke the Law, or turn them over to the police.
Although there was a limited Old Testament mandate to enforce the Law within the boundaries of the Nation of Israel under the Old Covenant, that covenant and nation was smashed and scattered hundreds of years before Jesus came.
Jesus specifically did NOT restore the true Theocracy of Israel when he came the first time (cf. Acts 1:7), and therefore did NOT set up a law-enforcement system to employ His Christian followers.
The question of self-defence is taken for granted in the New Testament however. Jesus warns His own followers to take steps to save themselves in times of persecution, such as fleeing to hide in the hills, or owning a sword for self-defence or deterring the crime of robbery.
There has never been any 'blood-guilt' for killing a man who invades your home at night in the process of defending your home and family. Jesus apparently did not directly address this question or change our obligations in response to emergencies such as a home invasion.
This means that robbers who invade occupied homes know full well their own risk in doing so, and can be assumed to be violent and dangerous men.
But most Christians would agree that violence or force is a last resort, and suggests that not only has all else failed, but somehow we have failed too, in addressing a problem before extreme behaviour is felt necessary.
For instance, in previous ages, people were 'imprisoned' for debt, which is self-destructive, since no one can pay off a debt while in prison, even by working.
The Law was rightly changed to reflect common sense and more Christian values, and 'debtor's prison' was abolished.
In many cases, our laws are not really inspired by the Holy Spirit, nor is their enforcement. Often we have to find ways to change the law, or change its application or penalty, to reflect better the Christian world that God wants us to build.
To address your question directly, I would say that NO scripture, even in the Old Testament gives citizens the right to 'vigilante justice' or to enforce the Law themselves, except in emergency situations, like a break-in.
On the contrary, Israelites are warned to obey the courts and the judges and rulers of their people, and make the best of it.
In the New Testament, men are called to such a high and difficult standard that they may even be expected to suffer loss of their property, even their families, personal injury, and even torture or death in the process of serving God. This is hardly a mandate to kill others or enforce 'the Law', but rather a demand from God to live your life always as a living personal sacrifice in your employment in God's 'army' of servants, prophets, teachers, elders etc. there appears to be no specialized jobs like a physical 'policeman' or 'soldier' in God's 'elect', under the New Covenant.
Instead it is a serious adult commitment to a kind of 'warfare' which is entirely Spiritual, and not based upon earthly physical force or violence.
As Jesus said,
"My Kingdom is Not of this world."
The most effective weapons we are given in our spiritual battles for God are SPEECH and PRAYER. Although both seem foolish and inadequate to non-believers, believers should know from experience that both are very effective tools for change.
These are your weapons. use them wisely.
