I do not necessarily have a great awareness of the Church of Christ's traditions or beliefs. I would argue, however, strenuously with them that baptism is essential for salvation. One text strikes me as rather important along these lines: 1 Cor 1.14-17. Paul says that he thanks God that he did not baptize very many folks because God sent him to proclaim the gospel. He is arguing against the Corinthians who were proclaiming allegiance to certain factions because of who the baptizer was, etc. But the point that is valuable for us today is that Paul is disassociating baptism from the gospel. The implicit contrast shows that baptism is not an essential part of saving faith.
Beyond that, I would say that the Churches of Christ have a naive biblical primitivism that keeps them from asking the right questions. They essentially argue that since there were no unbaptized believers in the NT (generally true, with one or two notable exceptions) that this practice must equate to a principle. But that is hardly necessary, and results in some truly whacky conclusions if applied in other areas. Further, once one begins to think about the nature of the cross and what Christ accomplished, adding more requirements than trust in Christ to save is seen as adding to the gospel. Indeed, I will be so bold as to say that when we add any of our own works to what Christ has done we diminish the value of the cross and elevate the ability of sinners beyond what they truly are capable of. The whole NT wreaks of this message, even though one might not find it in a chapter and verse (though several come close).