In my experience, every Scriptural interpretation, no matter how contradictory to competing interpretations, is proffered with the explanation that it is was arrived at by the light of the Holy Ghost that resides in each believer.
What ever each “private” level a believer may be at in the eyes of God...all Christians who believe in Christ should hold at their root faith a certain core set of truths that are unwavering and are shared by all in the main. Two are key...the acknowledgment of Jesus Christ as being Lord by an oral confession of faith, and a belief in the heart that God has raised him from the dead. A repentance from a former sinful life must be evident and baptism by water and by spirit are also very necessary. There are several different creeds from antiquity, such as the Nicene creed which sum up those core values very nicely. Yes, I’ve attended Baptist churches in my life that would recite those creeds in their worship services quite regularly and several were printed on the inside binders of their Baptist hymnals. So, whatever...”private pagan” interpretations you think some Baptists indulge in, you have no idea of the dimensions of the core shaping values that God is writing on many of their hearts.
After all, if understanding scripture is truly of no “private interpretation”, then are we truly to trust even fallible human Popes to foster spiritual wisdom when God has himself said “and I shall write my laws in their inner parts.”? True, God has set various men in their places of authority, but he is also known to smite shepherds and scatter sheep when the shepherds themselves have gone astray. What shall sheep do when their shepherds have lost their vision?