Does "no part of this world" mean no involvement in politics? Jesus is reported as having said that his kingdom was &quot;no part of this world&quot;, and further of assuring Pontius Pilate that his followers posed no risk to the secular authorities. Given that, should Christians be involved in politics?

My kingdom is no part of this world. If my kingdom were part of this
world, my attendants would have fought that I should not be delivered
up to the Jews. But, as it is, my kingdom is not from this source.
John 18:36. NWT
Christians throughout history have differing interpretations of how the faithful should approach civil governments. I would point you toward a seminal work addressing this topic called Christ and Culture by H. R. Niebuhr. 

One position (Christ against culture), advocated by those like Mennonites, argues for total withdraw from the political sphere. Another position (Christ of Culture) sees politics as interwoven in salvation history and essential for Christian life. 

Niebuhr goes on to list three other interpretations. Each, I would argue, are biblically viable and have strong places in the history of doctrine.

So, this is certainly an important question. And Christians of all traditions will answer it very differently. It is also a Biblical question. And Christians of all traditions will interpret the Bible differently as well.

As you study and make up your mind, please remember this is far from a clear-cut issue. Some of the answers already posted strike me as approaching an unhealthy, black-and-white dogmatism.