Religions that say they are the sole true path to salvation need to concentrate on their unique points to prove they alone are acceptable to God. For this reason JWs seem to use the point that they do not get involved in politics as proof that they are special.
In the Old Testament there are a number of examples of followers of Jehovah being involved in politics, so obviously it can't be that bad. What about the New Testament? Is there anything to show that voting or political involvement is wrong?