To say that Christians cannot have a say in the laws and policies that God himself requires them to live under (Rom 13:1, I think) seems wrong. Further, to say that Christians can't have a say in the leaders who enact those laws and policies seems equally wrong.
Voting does not, in and of itself, mean you are against God's Kingdom, which isn't ruling over us yet. All we have as of now are the "superior authorities" that God has appointed.
So yes, I think Watchtower has gone way overboard on the neutrality issue.