It is very important to answer this question carefully since what the Bible means by the phrase “church of Christ” is not what the querist means when he uses the same phrase. In the New Testament, the word “church” comes from the Greek (EKKLESIA), meaning “the called out.” The church of Christ is the “called out of Christ”. The phrase simply refers to those whom Christ has saved. The phrase is used concerning all whom Christ has saved throughout the world (Compare Ephesians 1:22-23 with Ephesians 5:23). The phrase is also used concerning individual local groups of Christians who identify themselves with Christ (Romans 16:16). These local groups certainly do not make up all who are saved.
On the other hand, the person asking this question is not thinking of the phrase “Church of Christ” in the same way the Bible speaks of it. They are thinking of a “Church of Christ” denomination. While it may be argued that a Church of Christ denomination exists, those who are Christians and want to follow only the scriptures, will not be affiliated with such a group. Therefore, our immediate answer to this question should be “No.” No, we do not believe that only those in a Church of Christ denomination will be saved. What we do believe is that only those who follow Christ alone and keep His commandments are a part of His church, His called out body. It is only these people who will be saved (Matthew 7:13-14; 21-27). The question before us is not which church is going to be saved, but what must we do in order to be saved and thereby be a part of the Lord’s church. The Lord will save His church (Ephesians 5:23), those who have obeyed Him and been added by Him to His body (Acts 2:47).