Here are the reasons for being politically neutral.
In the wars, Christians in German are not going to kill anyone from other countries, including their brothers and sisters in the faith and Christians in these other countries won't kill anyone else, including their brothers and sisters.
Politics divide. Can you imagine the elders or COs or DOs or GB talking politics and telling people for whom to vote and not vote? There would be divisions in the congregation and the organization. Being politically neutral (or at least silent about it) prevents any of that.