Everything in this dispute rests on a question of method that both sides inherited and neither invented. Given a text that commands one thing and says nothing about another, is the unmentioned thing forbidden or left free? The Churches of Christ answer that a specific command excludes its alternatives: when the New Testament letters tell congregations to sing, in Ephesians 5 and Colossians 3, the command specifies the music the church is authorized to make, and adding an instrument is not obedience plus something extra but a different act than the one commanded. Supporting arguments are marshalled from history rather than from taste.
The Greek and Latin churches sang without instruments for centuries; the organ entered western worship late; and Reformed writers including Calvin argued against instruments on grounds close to these, which is why the position is not an American frontier eccentricity but a recognizable descendant of the older regulative principle of worship.
The opposing reading, held by the Disciples of Christ and by most of Protestantism, treats matters on which scripture is silent as expedients committed to the church's judgement, in the same class as the hour of the service, the language of the sermon, or the existence of a building. On that reading an instrument is no more an addition to worship than a hymnal or an electric light. Neither side can settle the matter by appeal to scripture, because the disagreement is about how to read scripture, and both sides recognize only that authority.