Some in the twitterverse have suggested or implied that applying bound conscience ends up replacing scripture with experience. Certainly history has shown time and time again, when other factors triumph over scripture, whacked theology and abusive practices show up in spades.
By the same token, experience does play a role in scriptural interpretation. Wesley’s quadrilteral, ie, scripture, tradtion, reason, and experience is very true even for Lutherans, but how we implement it is different. We like to discard the quadrilertal, and say scripture alone… but to be totally honest, if we threw out everything but scripture, we’d likely be in a vastly different place. Imagine if each parishoner had to reinvent the Augsberg confession from scratch, or even the Nicene Creed for that matter.
This is not to say tradition, reason, and experience should triumph, or even balance with scripture. But more so, I think we must admit they do play a role, even if only a small part in our interpretation.
As far as divergent beliefs, we can look towards our own recent history of a couple hundred years. We had pietists, rationalists, pro-slavery, anti-slavery, high church, low church, Missourians, anti-Missourians, and a host of others (the term election controvery is commonly used, but that seems merely a catch-all phrase to me). Then throw in that within some communities, there was a mix of Mormon and Reformed theology within the Lutheran church as well… yet if asked, many likely would say, scripture alone.
In light of such diversity, it is commonplace for there to be divergent thoughts on any number of issues over interpretation. Both sides will state they have the right interpretation. Both sides will provide solid scriptural support for their views, albeit each side likely will doubt how solid that support really is on the part of the other side, even more so if they use differing methods of interpretation. Some might even get out a hammer to pound their view into the heads of the other party, but to no avail.
This is where bound conscience enters in. I think Luther said it quite well.
Luther: For I am neither arrogant nor so eager for vainglory that for this reason I would be ashamed to revoke ill-founded doctrines. Indeed, it will please me most of all if the truth is victorious. However, I do not want to be compelled to affirm something contrary to my conscience, for I believe without the slightest doubt that this is the meaning of Scripture.
Luther: Unless I am convinced by the testimony of the Scriptures or by clear reason (for I do not trust either in the pope or in the councils alone, since it is well known that they have often erred and contradicted themselves), I am bound by the Scriptures I have quoted and my conscience is captive to the Word of God. I cannot and I will not retract anything, since it is neither safe nor right to go against conscience.
When 2 parties are thus at odds over an interpretation, both likely hold views very similar to Luther. In effect, if one wants to maintain some sense of unity, the really only solution is to agree to disagree, and in doing so respect one anothers views. A Hammer has no place in this.
Luther quotes taken from
http://www.elca.org/~/media/Files/What%20We%20Believe/Social%20Issues/In%20Process/Human%20Sexuality/Wengert_on_Bound_Conscience.pdf