In the first place we should never speak of "church of Christ doctrine" because, scripturally speaking, it doesn't exist. The New Testament does speak of the "doctrine of Christ" ("Whoever transgresses and does not abide in the doctrine of Christ does not have God" - 2 John 9). Doctrine does not come from Christ's church. Doctrine comes from Christ.
Still, some have said that "Church of Christ doctrine is way too restrictive." Several years ago The Tulsa World reported: "A once prestigious south Tulsa church has voted to renounce the Church of Christ, which among other things, bans instrumental music in worship and limits church offices to men." One of the church members while being interviewed said: "Some felt the ties with the Church of Christ were too confining. It was tying some down and keeping others out. Now the body is wanting even more freedom in worship, women's roles - things of that nature."
The truth is that the Scriptures (Christ's doctrine) were too confining for them. There is no "Church of Christ doctrine" which "bans instrumental music in worship and limits church offices to men." The Scriptures do that.
I've heard people complain because "the church of Christ" will not allow them to participate in drinking parties. It is 1 Peter 4:3, not the church, which will not allow true Christians to take part in drinking parties.
Dear God, give us all the heart of a servant so that we might abide in Your Word.