This is such a great question. I think the best way to answer it personally is to say I don’t believe in private interpretation of scripture. That can be very dangerous and is why we have non-theological, non-seminary trained people like Joel Osteen preaching their brand of Christianity.
RC Sproul explains this issue so well. He states that the Church never really wanted the laity reading scripture for fear of exactly what we have today. Denomination upon denomination. Growing up Roman Catholic I can remember learning that the Bible wasn’t really meant for the lay person. Now that we have so many great english translations it’s much easier to read although still very tricky to interpret in some areas. Sproul preaches interpretation of scripture within the confines of the church not privately. There’s only one right interpretation of scripture although there could be thousands of applications of it.
One thing our church preaches is agreeing on the essentials and not worrying about the non-essentials. So then that begs the question what are the essentials for our salvation. Christ says to have faith like a child. I think if we take that approach and lead our lives in a Christ-like fashion we can never go wrong. I know I’m not directly answering your question as to who has the final say or who is the final authority. To that question I will say the final authority is GOD. HE alone is the final judge.
So although some denominations may mis-interpret scripture I believe GOD sees into our hearts and knows our true intentions. That’s what we will be judged upon. I don’t believe if someone is not submitting to the authority of the pope and the teachings of the magisterium that it impacts their salvation. Unless of course someone is outright rejecting Christ. But believing or not believing that Mary was a perpetual virgin, or sinless vs sinful has no impact on my salvation. The Catholic church itself admits that they have developed a further understanding of scripture and therefore create doctrine surrounding it. So then you can’t constantly hold people accountable for something that continues to develop. Hence the essentials vs non-essentials. I believe the essentials for salvation are clear and will never change. If they were always developing then that would mean GOD is withholding information from us. For folks then who believed in Christ right after HE died 2000 years ago it means they had less information than we do placing their salvation in jeopardy. I find that hard to believe.
Hope that helps