Typically the authority of scripture is reflection on the "truth content" of the Bible's historical accounts and doctrinal/theological assertions. And there is no consensus now or likely ever about that. I think there may be different and better ways to think about biblical authority.
If we take our cue from the grain of the Bible as we find it in Gen.12:1-3, I suggest we think of the Bible's authority as its divinely given capacity to "author" communities who look like Jesus. This means that we will not first look at a church's theological statement to see if they have an adequate view of biblical authority. Rather, we will look at the way of life they pursue, the disciplines they practice, the quality of their community, and how they act to spread the blessings of God to the rest of the world. Doubtless the theological views of different communities will continue to vary but we will learn to read their lives in a way that we can discern whether they possess a "family likeness" to Jesus. If so, we will trust they are living "under biblical authority."
Consider the Ten Commandments (Ex.20:1-17). We tend to think of these as general commands for everyone that teach us how to be good or moral people. We post them on courthouse walls and treat them as abstract ideas we ought to promote. That is, we treat them as if their purpose is basically to regulate human conduct. Such a reading of the commandments, however, fails to understand their significance in the biblical story.
The Ten Commandments are given to an Israel that owes its existence to the gracious initiative and power of its God. The commandments are given to shape and structure the life of this community of the redeemed. They were never intended as a universal generic code of ethics. These commandments are given to "author" a people. A people whose distinctive way of life will demonstrate to the rest of the world what God means human life to look like. Their "authority" resides in God's intention to use them this way. To stand under their judgment is to acknowledge breaches of community we have committed.
The commandments form the life of a people to reflect what God intends for everyone. But we can only come under this "authority" through embracing the same relation to its God and way of life that Israel did. If we continue to try and impose the Ten Commandments on a pluralistic public we misuse them and damage the credibility of the church as well.
This view of biblical authority will doubtless seem too weak to some, too judgmental to others, and impractical to most. We are not well practiced at this type of discernment. But I believe we must learn this skill. This too brief and still evolving vision of biblical authority has important implications in other areas as well. At any rate, I think we all need to struggle to find ways to learn to identify and affirm communities that live out that "family resemblance" to Jesus in spite of their differences in theology.