I wish I could be of more help with this, and I am mainly chiming in because nobody else has...the reality is that the book "Celebrate Liberty" is not one most people are familiar with because it is not entirely common. I tried to figure out which Adam's speech is used in it but couldn't determine that.
So why am I writing if I don't know the book? Well, despite that, I do know about John Qunicy Adams' religious views, so that might be of some use to you. I don't know specifically what he says in your speech, but Adams was a Unitarian.
What that basically means is that he did not believe in the Trinity. Unitarians also believe that the Bible contains possible flaws (because it was written by men) and that there is no such thing as original sin.
For Adams, part of this was an argument against slavery (which was a big issue of the time.) He did not feel that the Bible justified the modern practice of keeping slaves, despite the fact that some people in the Bible kept them.
I hope this at least gives you some thoughts in the right direction.