"What I think it means is that this world is owned by this world... We are not here for any of it. You notice Jesus was not violent, but was very involved socially and somewhat politically at times. He was here to do spiritual warfare, not physical. The same for us, and Caesar represents the world. Let the world have what is theirs. Let God have what is his. Material/carnal vs. the spirit.

Quoting things like that is usual mistake made from listening to false teachers.
Luk 20:25 And he said unto them, Render therefore unto Caesar the things which be Caesar's, and unto God the things which be God's.

So what is God's?
Psa_24:1 On the first day of the week, a psalm for David. The earth is the Lord's and the fulness thereof: the world, and all they that dwell therein.

Deu_10:14 (DRB) Behold heaven is the Lord's thy God, and the heaven of heaven, the earth and all things that are therein.
So the world is owned by God, not by the world.

Yet I suppose Jesus said this for no reason:

Luk 22:36 He said therefore to them, But now he that has a purse let him take it , in like manner also a scrip, and he that has none let him sell his garment and buy a sword;

Since He knew the perils of times, that were to come.

Even so, He will return as a Warrior/King, subduing his enemies with a sword, not with non violence or nice words.

Are not Christians supposed to try to be like Him?"

I was looking for that verse. Thank you Anonymous Coward 39081868.