It's a little counterintuitive. I vote with the intent of limiting the commingling of government and religion, because of my religious beliefs. Weird, huh?
As to your second point, not to start a war here, but I believe that to be a christian you have to be christ-like. To be christ-like is to be non-violent and to turn the other cheek. So, I reject the idea that any true christian ever advocates war.
The confusion among 'christians' is a result of people putting their own wants, opinions and logic ahead of what God commands. There is no confusion for those who accept the word and live by it, even in the face of their own experience. For example, Paul said that the world considers preaching foolishness, but God commands it. When we think about things and arrive at conclusions other than what the book teaches, then we are being worldly and not spiritual. I understand that may sound like a lot of crap to someone who does not believe. If you want to get into the reasons for belief, I think we need to take it elsewhere, but I would be happy to oblige.