Are those who go to the church of Christ the only ones that will be saved?

The Lord's church is the body of Christ, (Colossians 1:18).  If one is not part of the body of Christ, which is the church of Christ, then one is not saved because Jesus is the savior of the Body, (Ephesians 5:23).

Now, one must ask, is the church of which I am a member doing what it needs to do to be part of the body of Christ? If it isn't, then it isn't part of Christ's body; If it is, then it is part of Christ's body.

The name that the church puts on the sign is only significant in that it can tell you whether or not a particular church is NOT part of Christ's body. For example: If you see a sign that says "St. Paul's Church" then you know it isn't part of Christ's body because Paul the apostle said not to do something like that in 1 Corinthians 1:10-13. So one could conclude the same regarding any name that isn't found in scripture.

However, merely because the name "CHURCH OF CHRIST" may appear on the sign (or any other biblical name, for that matter) doesn't prove in any way it is a church which is part of the body of Christ.   In order to be part of the body of Christ, a church must worship in the way Christ authorized us to worship, teach salvation in the way Christ said to teach it, be organized after the pattern that is left for us in the scriptures, and follow the pattern that God has left us in all things. That's what makes a church part of the body of Christ. 

For example; if people take the Statement of Faith from the Lutheran Church or the Catechism of the Roman Catholic Church, and follow these manmade documents, they are practicing those respective beliefs and are therefore affiliated with that man made denomination and are therefore either Lutherans or Catholics.  So any body of believers that acts according to the scriptures to serve and worship God is part of the body of Christ whether their name says "CHURCH OF CHRIST" or some other name that is scriptural in nature such as "CHURCH OF GOD" or "CHURCH BY CHRIST JESUS". 

Those who make this accusation that the "Church of Christ" is the only church going to heaven, assume something in the accusation. What they assume is that every congregation that takes the name "CHURCH OF CHRIST" is somehow affiliated together in an extra-biblical way so as to constitute a denominational body.  The only problem with this is that they can't prove it to save their lives. The churches of Christ are affiliated, but only in the sense that we seek to allow the Bible alone to determine our courses of action.  That's not affiliation in the same sense as the Methodists churches are affiliated under the UMC denomination or that some Baptist Churches are affiliated under the Southern Baptist Convention.

However, others see the unity that we have, which unity comes solely from the study of scripture, and assume that we couldn't have such if we didn't have some kind of extra-biblical affiliation. And so they conclude that we are a denomination just like them.  The truth of the matter is that those who desire to respect Jesus' standard for unity simply don't allow human opinion to influence that which is precious to them. As a result, this one central desire unites us in a way that no manmade religious organization could ever achieve.  This is why in the denominational world you simply do not find the concern for teaching sound doctrine as you find among members of the body of Christ.  It is also why if we ever give up that desire, we WILL become nothing more than another man made denomination.

Some who worship in denominational churches have stated, on occasion, that those who worship at a church of Christ claim that they are the only one's that will be saved.  Though this might be heard from some that attend a church of Christ, it should be noted that the general attitude of only being able to be saved by means of any "particular" religious affiliation can be attributed to most, if not all, of the denominations and other religious factions.  The only way anyone can be sure they are following the right path to God through their church affiliation is to study His word regarding His church.

2 Corinthians 13:5
Examine yourselves, whether ye be in the faith; prove your own selves. Know ye not your own selves, how that Jesus Christ is in you, except ye be reprobates?

See also:

The Value of the Church

Just Another Denomination?

Is One As Good As Another?

Variety in Religion