The Greek word translated "conversation" emphasizes "citizenship," with all of its attendant loyalties and expectations for appropriate behavior. The structure of the introductory word "only" indicates that it is an adjective, not an adverb. Thus, the opening phrase could be rendered, "Your only citizenship must be lived out so that it becomes the gospel."
The New Testament employs three different Greek terms that are translated "conversation." Anastrepho is best understood as "dwelling" or "remaining" in a certain place: "Put off concerning the former conversation," we are commanded in Ephesians 4:22. Tropos stresses the manner of life, perhaps implying the reputation one gains by the lifestyle: "Even as Sodom and Gomorrha, and the cities about them in like manner giving themselves over to fornication, and going after strange flesh, are set forth for an example (Jude 1:7). Politeuo, the term used by Paul in our text, conveys citizenship: "For our conversation is in heaven" (Philippians 3:20, politeuma). The emphasis of our text is on our lifestyle and testimony as "ambassadors" in a foreign land (2 Corinthians 5:20). As such, we are to live in a manner that "becometh" the gospel--"that ye walk worthy of the vocation wherewith ye are called" (Ephesians 4:1)
We are to stand fast in a unity of one spirit with one mind. Paul closed his letter to the Philippians with this: "Therefore, my brethren dearly beloved and longed for, my joy and crown, so stand fast in the Lord, my dearly beloved" (Philippians 4:1). HMM III http://www.icr.org/article/becoming-gospel/