The whole Bible is our creed
Campbell, in the Parable of the Iron Bedstead, was gently urging his brothers at the time to give up their human creeds and take the whole Bible instead. What he meant by that, though, is not at all what most restoration movement writers and preachers have meant by it in the 20th century. In the paragraph previous to the one urging the entire New Testament scriptures as our sole creed, he said, "Why not, then, dispense with this piece of popish furniture [the wheels and knives used metaphorically of human creeds as tests of fellowship] in the church, and allow Christians of every stature to meet at the same fireside and eat at the same table?"
He is advocating tossing our shorthand summaries and opinions of the scriptures as tests of association. Anyone who is a brother--and this is key in understanding the idea of open fellowship--and who professes to accept the entire New Testament as his creed is to be accepted around the fireside and at the same table. In this way, the creed (the scriptures) becomes a unifying thing, not a divisive thing.
This is not dividing the Bible into essentials and non-essentials, but taking the entire thing as authoritative. I make a distinction, as I think most do in practice, that the gospel, the good news that we preach to a lost world, is distinct from the apostolic teachings. This is true in the sense that appointing a plurality of elders is not a fact of the gospel that Peter preached to create converts to Christ, bringing them into koinonia, yet it is a valid deduction from the apostolic letters that those in the fellowship of Christ ought to put into practice when they learn it.
The gospel is the message preached to bring one into union with Christ and the citizens of his kingdom, while the apostolic letters are the divine messages addressed to the first century congregations of believers to encourage them and to fix various problems that had arisen. The gospel, and obedience to it, is the entrance exam to the Kingdom (a true test of fellowship), while the apostolic doctrine is the curriculum, the course of study for the King's subjects.
To the citizen of the Kingdom, the entire NT scriptures are binding. The question is, who binds them and how? I believe they are binding insofar as our individual consciences and intellects apprehend the teaching. I think many of us recognize this, but haven't really thought it through until now. For instance, while we may generally agree that a plurality of elders is inferred and can be deduced from various passages, we don't exclude whole congregations from the Kingdom who have no elder yet, or who only have one elder. We simply do what we can to fix the situation.
Here's a shocker for you. Do I believe Jesus' unequivocal command for the disciples to wash each others' feet is binding? Yes.
This command and all other commands are binding insofar as our individual consciences and intellects apprehend the message. One person believes he is following the Lord's will on this by washing the feet of his brethren. This is binding to him, because that is his conscience and the conclusion of his intellect on the subject. I believe I am following the Lord's will on that when I serve my brethren. This is binding on me, and I take it seriously.
Both of us use the entire NT as our creed, having different conclusions about a particular practice, but fully accepting each other as faithful brethren. That is the model for unity that I believe the Bible teaches, not segregating into "foot-washing" factions and "non-foot-washing" factions. This model for unity is the one advocated in Romans 14.
The creed question expressed in the bedstead parable dates back to a time when the Lord's supper would not be given to someone unless they assented to the creed of the denomination. It was quite literally a "test" of fellowship, with congregants being forced to take a test on the creed of the group if they wanted to "take communion." So when Campbell talked about using the entire NT as our only creed, he was not talking about assent to some person's unique conclusions about the entire NT (which change over a lifetime as we grow) as a test of fellowship. He was talking about the profession of assent to it in its entirety as a test of fellowship.