Consider a few questions:
Do you, a Christian, believe it would be wrong for you to kill another Christian?
Do you, a Christian, believe there are other Christians all over the world?
Do you, a Christian, believe it would be wrong for you to go try to find Christians in another country and try to kill them?
If you answered "yes" to them all, then what difference would it make if you had on a military uniform while you were doing it? It may be that your country hasn't ordered the military to sniff out Christians specifically, but you are shooting bullets into groups of people which could include your brother in Christ. Do you think it's okay to kill other Christians if you did so as part of your country's military campaign in the country where those other Christians reside?
If you think a government-ordered military campaign makes it okay to kill other Christians (even unawares), how have you not implied that your loyalty to your country is greater than your loyalty to your brothers and sisters in Christ?