I dont know if it was intentional or not, but I did find this post to be a bit “rude”. To me it comes accross as being somewhat disrespectful of others beliefs and a tad condescending.
I could be wrong, but I am only expressing my opinion.
To try and answer your question, I can only speak for myself and not everyone else, it depends on the dispute. Generally I seek advise from others, pray, try to see things in a non-objective way (as well as from other parties point of view) and refer to the bible.
I think that it is better to look for the right solution rather than the solution that makes you right.
It was not meant to be rude. I personally felt that to answer “Jesus Christ is my authority” when the OP specifically asked not to was rude and condescending.
While I believe that God does speak to us, we must be very careful what we listen to. If what we hear or if what we interpret from what we read in Scripture differs from what has been taught by the Apostles and their successors throughout the centuries, the source is probably not God. Remember that the devil prowls the world in search of souls to devour. This is where Authority comes in.
I genuinely want to know how those who say they have no earthly authority decide doctrine, say what Communion is or if you even have it at all, for instance. Catholics say it is truly the Body and Blood of Christ, others say it is merely symbolic. How do you determine the Truth? This is very important. Your immortal soul depends upon it.
Who determines what is taught to your children at Sunday School? Where does your doctrinal statement come from, who says that it is the Truth and by what authority?
What it boils down to, for me, is that if Jesus is not speaking to you directly, then you must be relying on the personal interpretation of people in your church, either the founder, your pastor, the whole congregation, a committee, or yourself - an earthly authority whether you admit it or not.