Paul seemed quite happy to lobby the Governments of his day
You quote "no part of the world", a phrase that is only found in John (15:19; 17:14,16; 18:36).
The context is that since Christians are chosen out of the world, to a relationship with God, the world doesn't like them very much.
The phrase has taken on an altogether different connotation under the WTS.
The argument goes that Jesus took no part in politics, and when they tried to seize him to make him king he ran away. Even so, he entered Jerusalem in the manner of a king, and admitted before Pilate that his kingdom was not of this world (John 18:36).
I find it incongruous that the WTS denies it's members the right to influence governmental rule, but is quite happy to endulge in helping form the legislation of various countries, through the law courts.