“It’s acceptable for Christians to be in the military because Jesus never told the centurions to stop what they were doing.”

No


When Jesus heard this, he was amazed and said to those following him, “Truly I tell you, I have not found anyone in Israel with such great faith. I say to you that many will come from the east and the west, and will take their places at the feast with Abraham, Isaac and Jacob in the kingdom of heaven. But the subjects of the kingdom will be thrown outside, into the darkness, where there will be weeping and gnashing of teeth.”

Then Jesus said to the centurion, “Go! Let it be done just as you believed it would.” And his servant was healed at that moment. Matthew 8:10-13

Jesus commended one centurion for his faith—not his occupation. Jesus also never told the “woman at the well” that she was wrong for having five husbands—and divorces, as well as living with a man who was not her husband. Neither is there any record of Jesus directly telling prostitutes that they were in the wrong profession but that doesn’t mean he commended it.  Each of these things are covered in his teachings, which he clearly had in mind for his followers to obey, whether he made a direct, personal application to them individually or not.

Jesus taught:
“Love your enemy.” Matthew 5:43-48

“Bless those who curse you.” Luke 6:28

“You have heard that it was said, ‘Eye for eye, and tooth for tooth.’ But I tell you, do not resist an evil person. If anyone slaps you on the right cheek, turn to them the other cheek also.” Matthew 5:38-40

“My kingdom is not of this world. If it were, my servants would fight to prevent my arrest by the Jewish leaders. But now my kingdom is from another place.” John 18:36

Peter said, “Do not repay evil with evil or insult with insult. On the contrary, repay evil with blessing, because to this you were called so that you may inherit a blessing.” 1 Peter 3:9

Paul said, 
“Do not be overcome by evil, but overcome evil with good.” Romans 12:21

“For though we live in the world, we do not wage war as the world does. The weapons we fight with are not the weapons of the world.” 2 Corinthians 10:3, 4

“For our struggle is not against flesh and blood, but against the rulers, against the authorities, against the powers of this dark world and against the spiritual forces of evil in the heavenly realms.” Ephesians 6:12

Jesus’ expects his followers to be different because they’re not operating the way this world does, but in God’s way.  By not telling the centurion—just one man, that he shouldn’t be in the military, Jesus did not wipe out all of his teachings about loving ones enemy.

“If you hold to my teaching, you are really my disciples. Then you will know the truth, and the truth will set you free.” John 8:31,32

"Whoever has my commands and keeps them is the one who loves me. The one who loves me will be loved by my Father, and I too will love them and show myself to them.” John 14:21

Jesus replied, “Anyone who loves me will obey my teaching. My Father will love them, and we will come to them and make our home with them. Anyone who does not love me will not obey my teaching. These words you hear are not my own; they belong to the Father who sent me.” 
John 14:23,24

Obeying the Authorities/Going to War

“Since The Bible Says to Obey the Governing Authorities, Christians Must Be in the Military and Go to War.”
Yes to the first part--no to the second.

The Bible does indeed say that we are to “be subject” to the governing authorities:
1 Let everyone be subject to the governing authorities, for there is no authority except that which God has established. The authorities that exist have been established by God. 2 Consequently, whoever rebels against the authority is rebelling against what God has instituted, and those who do so will bring judgment on themselves. 3 For rulers hold no terror for those who do right, but for those who do wrong. Do you want to be free from fear of the one in authority? Then do what is right and you will be commended. 4 For the one in authority is God’s servant for your good. But if you do wrong, be afraid, for rulers do not bear the sword for no reason. They are God’s servants, agents of wrath to bring punishment on the wrongdoer. 5 Therefore, it is necessary to submit to the authorities, not only because of possible punishment but also as a matter of conscience.
6 This is also why you pay taxes, for the authorities are God’s servants, who give their full time to governing. 7 Give to everyone what you owe them: If you owe taxes, pay taxes; if revenue, then revenue; if respect, then respect; if honor, then honor. Romans 13:1-6

However, these “authorities are God’s servants”(v.6) put in place by God for his purposes.

The Son is the image of the invisible God, the firstborn over all creation. 16 For in him all things were created: things in heaven and on earth, visible and invisible, whether thrones or powers or rulers or authorities; all things have been created through him and for him. Colossians 1:15-17

Since these authorities are “created through him and for him”, they are to be submitted to only when they don’t tell us to do things contrary to what Jesus has taught.

Peter and the other apostles replied: “We must obey God rather than human beings!
Acts 5:29

There may be punishment for following Jesus rather than the authorities but we must follow Jesus because he is the final authority and judge. When Christians join the military or in the event of a draft, submit for duty—against Jesus’ and his disciples’ teachings of loving ones enemy (Matthew 5:43-48) and overcoming evil with good (Romans 12:21), those who do follow Jesus’ teachings and refuse such things at greater peril of punishment.*

*See “Christians should be proud when their sons and daughters join the military and go off to war.” http://urbanlegendsbible.blogspot.com/2011/11/christian-soldiers.html

Christian Soldiers?

“Christians should be proud when their sons and daughters join the military and go off to war.”

No

Jesus said just the opposite. There is no way that shooting or bombing one’s enemy (or anyone) is loving them or blessing them—the enemy or the one who kills their enemy. As long as people kill each other in retaliation, the killing will never stop. Jesus has a better way in mind; Christians are, rather, to set the example:

“Love your enemy” (Matthew 5:43-48).

“Bless those who curse you” (Luke 6:28).

“You have heard that it was said, ‘Eye for eye, and tooth for tooth.’ But I tell you, do not resist an evil person. If anyone slaps you on the right cheek, turn to them the other cheek also” (Matthew 5:38-40).

Peter said, “Do not repay evil with evil or insult with insult. On the contrary, repay evil with blessing, because to this you were called so that you may inherit a blessing” (1 Peter 3:9).

Paul said, “Do not be overcome by evil, but overcome evil with good” (Romans 12:21).
Jesus’ expects his followers to be different because they’re not operating the way this world does, but in God’s way.

Jesus said, “My kingdom is not of this world. If it were, my servants would fight to prevent my arrest by the Jewish leaders. But now my kingdom is from another place.” (John 18:36)

Paul said, “For though we live in the world, we do not wage war as the world does. The weapons we fight with are not the weapons of the world” (2 Corinthians 10:3, 4).

For our struggle is not against flesh and blood, but against the rulers, against the authorities, against the powers of this dark world and against the spiritual forces of evil in the heavenly realms (Ephesians 6:12).

If we “resist” or kill an “evil person” the effect is like cutting off the top of a weed without digging out the roots—it will come back. Jesus’ way is to fight the devil instead—to get to the root of the problem with the spiritual “weapons” of prayer and love.

Finally, Jesus told his disciples, “Put your sword back in its place,” Jesus said to him, “for all who draw the sword will die by the sword” (Matthew 26:52).

I don’t at all mean to sound harsh but only to convey what Jesus said—if you encourage your children to join the military, don’t be surprised if they die there. Even if they make it back home, they will have died to some degree on the inside. Jesus has called us to a better way--that of following his teachings.

To the Jews who had believed him, Jesus said, “If you hold to my teaching, you are really my disciples. Then you will know the truth, and the truth will set you free.” John 8:31,32