To answer that question, there're a few foundational things to
deal with....
First of all, the answer has nothing to do with the differences
between the NT and the OT.
The bible is ONE, and God is the same throughout the ages, He
never changes today or tomorrow.
The differences between the Old and New Testament is a matter of
covenants and ceremonies. For example, in the Old Testament, before
Jesus came to wash away sin through His blood, the ceremonies and
festivals were necessary as a symbol of how the Lamb of God will
redeem us, but after He has come, there is no longer a need for
such ceremonies...and so on.
However, the character of God is the same throughout the NT and
OT. The law is still valid, in the OT and NT, although both in the
NT and the OT, nobody could be saved by the law, but these are
eternal truths of God's character that does not change.
So the concept of a difference of whether it is right/wrong
after OT/NT is a wrong concept and in theology, it is a type of
heresy to believe a seperate character of God in OT/NT.
Back to the question on whether Christians can be soldiers. As
in all things, it is according to your faith, whether right/wrong,
the laws of God are plain to read, the commandments of God, not to
kill the innocent, etc. are plain.
But whether joining your nation's army is right/wrong is a
matter of your own discernment/faith, if your country's military
force is for the peace of mankind and nations, or for destruction
and the use of satan.
A few scriptures to consider:
In Ecclesiastes, it says, there's a time for
everything....including for peace/war.
In the OT, the children of Israel had an army.
In the NT, the nations in the end times were judged according to
which side their army was on, for or against Israel.
In Revelations and throughout the bible, God has an army too -
of angels.
So....I think we can conclude, throughout the bible, there's
nothing against an army/military force. Just like you can be rich
and be righteously rich like David, or you can be poor but a
sinner. Rich or poor doesn't mean if you're right, so army or not,
doesn't mean you're righteous or not either. It is a matter of what
you use your military force for, just like money, or anything
you're given in this lifetime.