In an online debate with John Frame about the Regulative Principle of Worship, D.G. Hart wrote about ordained ministers differing with the confessional standards to which they vowed subscription:
But what happens if my study of the Bible, the counsel of friends, a particularly good sermon, or even a ruling of the Supreme Court persuades me that the Standards are wrong? Do we have any means to revise the Confession and catechisms? The answer is of course. But the way to revise is not simply in my own mind, or in consultation with my editor, or by testing my views in the publishing market. The way to revise creeds is through the church, specifically through the Presbyterian system of graded courts. So first I tell my session (as an elder) or my presbytery (as a minister) of my new views. If they conclude that my views are outside the bounds of the Standards, then either I resign my office, or I write an overture to call for a revision of the Standards. And then I try to persuade the church. Should I fail in my effort I can either resign or force the church to try me for teaching views contrary to the Standards.
For non-denominational churches with a fairly short official confession for membership and another document outlining the teaching position of the church, I suppose the same would apply. If I’ve signed (i.e. sworn) to something like this, the above is what I do.
So, that answers my question a few months back – at least for me – about confessional dissonance.