Depends on one's convictions. Many do not vote, would be excused from a draft, and do not serve jury duty. Others do all of the above.
Scripture demands that we act in such a way befitting our status as citizens of another kingdom (as sojourner, or aliens, here).
Scripture does not demand we vote, serve on jury duty, or serve in the military.
Whether Scripture prohibits those things is an issue for the individual Christian.
We (Christians) call God our Father while acknowledging He is also a Judge who will impartiality judge our deeds - so there is a fear and care when considering these things.
Each of us will have to account for our choices. So, IMHO, each should make their own choices.