Before we can make the world we want, we need to be honest with ourselves about the world (and people) as it is (they are)
Much to our relief, we discovered we did not need to consider another's conception of God.
When, therefore, we speak to you of God, we mean your own conception of God. This applies, too, to other spiritual expressions which you find in this book. Do not let any prejudice you may have against spiritual terms deter you from honestly asking yourself what they mean to you
I've been to many meetings (my rough estimate is 3042) and at nearly all of those we refuse to allow the Lord's prayer. The whole group exercises that tradition 2 you referred to and determines that we don't want to use it since it is tied to Christianity. We don't really give much consideration to an individual's expressed faith. (or lack thereof)
To be fair, there is wide variation across the whole of the fellowship, so as always YMMV
You see but you do not observe. Sir Arthur Conan Doyle, in "The Memoirs of Sherlock Holmes"