Church of Christ has some distinct things about it that separate it from other Christian Denominations. The first is they claim they are not a denomination but the extension of the one true church that Jesus created and is written about in the New Testament. Yet at the same time they claim they were formed around the 1830's. This is really no different than the Pentecostals, they say both of these same things. Well neither denomination is being honest because if they were Christ's one true church that was started in the Book of Acts, there would be no need for it to be formed again almost 2000 years later. (That's because Jesus said in Matthew 16:18 that the gates of hell would not prevail against His church, so if either of these denominations were the only true church, they would've been consistently in existence, with their distinct practices going on throughout Christianity's history.)
Let's look at some of the other distinctions of Church of Christ by looking at an overview I found on Got Questions?org.
One “minor” issue is the Church of Christ policy of not allowing musical instruments in their church services. While we entirely agree that a church is well within the freedom God gives to not use musical instruments in worship, the problem is that some within the Church of Christ are fanatically against musical instruments. Some are fanatical to the point of declaring any church that uses musical instruments as not being a true, biblical, or godly church. Such dogmatism on a clearly non-essential issue is often the mark of a cult, not the mark of a good biblical church.
A second issue is the fact that some in the Church of Christ claim to be “the one true church,” outside of which there is no salvation. By no means do all Church of Christ members believe this, but it is prevalent enough to warrant concern. Some go so far as to argue that since the name is “Church of Christ,” that indicates that the church / denomination is the one and only true Church of the Lord Jesus. This is completely unbiblical. There is no one church or denomination that encompasses the entire Body of Christ. The “one true church of Christ” is comprised of all those who have, by grace through faith, personally received Jesus Christ as Savior. The Church is composed of true believers everywhere, no matter the local church or denominational affiliation. The claim of exclusive access to salvation is another common identification of a cult, not the teaching of a good biblical church.
A third and very important issue is the Church of Christ’s emphasis on baptism as being necessary for salvation. Church of Christ advocates point to Scriptures such as Acts 2:38, John 3:5, Mark 16:16, 1 Peter 3:21, and Acts 22:16 as biblical evidence that baptism is required for salvation. There is no denying that baptism is very important. Baptism is intended to be an initial act of obedience to Christ, an illustration of Christ’s death and resurrection, a public declaration of faith in Christ, a step of identification with Him, and a proclamation of desire to follow Him. In the minds of the apostles and early Christians, baptism was so inextricably linked with salvation that the two were viewed as inseparable. The idea that a person could receive Christ as Savior and not be baptized was completely foreign to the early church.
Now for a very thorough understanding of the Church of Christ denomination from an inside perspective, please read this website written by a former Church of Christ preacher. He actually committed suicide due to the extreme legalism he suffered while at the church but God in His mercy miraculously saved him from death.
On this video this preacher brings up some very good points about the name of Church of Christ and how when they claim they are the extension of the one true church found in the Scriptures based on their name, it is not true: https://www.youtube.com/watch?v=bvWJdskywNI
If you want to get born again in Christ Jesus, please take this time now to talk to God. You can say something like this: God I know I am a sinner and I need a Savior and I believe Jesus Christ is the promised Messiah. I believe Jesus Christ was born of a virgin mother, conceived by the Holy Spirit, and that He lived a sinless life because He was God in the flesh, and that He was crucified as the once for all sacrifice for mankind's sins. I believe he was buried and rose from the grave and was witnessed alive before ascending to heaven where He now sits on the throne as King of Kings. I repent of my sins and accept Jesus' gift of salvation today and I ask Him to be my Savior and Lord. I ask the Holy Spirit to come and make a dwelling in my heart and to lead me into all righteousness. Thank you God for hearing my prayer and for sending your Son to save me by dying in my place at the Cross so I can be in the family of God. And Father, I understand that while I am saved by my confession of faith, it is also Your will for me to get water baptized to show my private confession in a public way, and so I ask you to lead me to the church or baptismal situation you have for me so I can get baptized in the name of the Father, Son and Holy Spirit. Amen!