There's two main factions within the Church of Christ denomination and only the smallest faction chose a cappela. The denomination itself, as a whole, also falsely asserts that unless a person has undergone water immersion baptism they are unable to be saved. This is a false teaching. A person certainly can be saved and experience the new spiritual birth without being immersed in water during baptism. I'll be happy to debate anyone on that point who says otherwise.
Other than those two misnomers, the Church of Christ fits into mainstream evangelical Christianity as part of the "Stone-Campbell Movement" which is the common term for an American reform effort that began in the early 19th century in both the United States and Scotland.
But you want to talk about musical instruments. Church of Christ will argue that musical instruments were banned from the early church on account of their worldly nature and that instruments in general were banned throughout the first century. They'll argue that in Judaism, musical instruments were banned after the destruction of the temple as a way of expressing disapproval over the temple being destroyed and cite Werner and say the primitive Christian community held the same view.
The truth is, as McKinnon explains, there is no actual emperical support (such as the Bible, early rabbinical writings, contemporaneous literature, etc...) that instruments were banned in the synagogue after the destruction of the temple and it's well documented that music with instruments (three main groups: strings, wind and percussion, also see Psalm 150) was an integral part of Hebrew culture and had its place also in religious life. For example, read 1 Ch. 15:16–24 which contains a detailed account of the organization by David of the levitical choir and orchestra.
Of course your "religious" faction of the Church of Christ will argue that they also engaged in animal sacrifice and various civic/ceremonial activities the Law of Moses required in the old covenant that we don't do anymore with Christ's sacrifice and the institution of a new covenant. But that's an obvious red herring. Bearing false witness was outlawed in the old testament, for example, so is the prohibition against bearing false witness no longer valid for today? Obviously it IS for God's morality is universal for all people for all times. Using musical instruments to facilitate the purposes of music such as worship, teaching, etc... does not violate God's universal morality: only their own "religious" conviction. I think you get the point.
They are correct; however, that some early church fathers (not all) did consciously strive toward the simple declaration of Scripture maintaining a music free from musical instruments.
But as Norden points out, singing hymns as spontaneous praise to deities in public assembly with musical instruments had been a common practice in Jewish and the pagan communities long before the New Testament era and some Pauline communities were musically oriented (see 1 Cor 14:15, 26) with members encouraged to teach and admonish one another with psalms, hymns and spiritual songs (Eph 5:19; Col 3:16). Elsewhere in the New Testament, and in the writings of the apostolic fathers, the allusion to hymns or songs and the discovery of hymnic fragments back to the third century provide windows to the hymns or songs used in other Christian communities during the first two centuries and they may very well have used musical instruments. It's non-sequitur to say the didn't given the use of musical instruments in the culture during that period both amongst Jews and non-Jews.
You're not going to change them, however. If you try, you'll be labeled a false teacher who has “gone liberal.” So, either accept their error which in this case is a non-essential meaning you can stay if you like or move on to a church that uses musical instruments. The choice is your own.
My denomination just calls themselves "Church of Christ", but I think so do other denominations, so it isn't very specific. I do agree that it isn't an extremely important matter, I was just wondering.