The term means a Quaker who honors and respects George Fox's admonition that we "let Christ be our teacher". Believe it or not many Quakers don't fit this category. How come? Basically because Quakers are the most inclusive religious body that you can imagine: everyone is welcome: unitarian, agnostic, atheist, buddhist, you name it. This was to a considerable degree because in the 19th century they had excluded so many that they were facing extinction (like the Shakers!). Like people so often do, the unprogrammed Quakers moved to the opposite extreme. (Most Quakers are thoroughly, aggressively Christocentric to the point of requiring Christ for membership; those are programmed Quakers, but I'm talking here about the unprogrammed ones, more apt to be in one of the 'blue' states.)
The programmed Quakers usually have a pulpit centered meeting house with a spouting preacher (in spite of George Fox's denunciation of 'steeple houses' and 'hireling priests'). I find them like real good Methodists, but the subject here is the unprogammed Quakers, actually something of a splinter group today, but one to which large numbers of bloggers belong.
The particular subject here is one particular unprogrammed Quaker, a flaming liberal and dear friend of ours named Alfred Ames. Alfred and I had much in common: both PK's (preachers kids); both kicked religion at an early age, but Alfred came back much sooner than I had done. In 1942 he had 'flat feet' and was declared 4F (draft ineligible); otherwise he would surely have been a CO (conscientious objector).
A young man in his twenties he had found his way into the Quaker Meeting (at Urbana, IL, I believe). The peace testimony has always been central among Quakers, but one of the head knockers at this meeting, an old gentleman, had a son who was a Colonel in the Marine Corps. He found Alfred's peace testimony so objectionable that he attempted to cast him out of the meeting. Alfred refused to be cast out. (When I knew him he referred to himself as a 'professional controversialist'-- a good term for a proud and confirmed Quaker.)
Alfred got his PhD in English Literature and sufficient command of the language that he got a job in the editorial department of the Chicago Tribune. You old heads know that the CT was simply the most troglodytic newspaper in the land in the mid 20th century. Alfred worked for that organ for 30 years; I guess he was the pet liberal.
We met Alfred when we moved south and took up the Brevard (NC) meeting, a hotbed of non-christocentics; no one ever used the language of Zion. Well I did, at every opportunity; frequently quoted the Bible. I came to see that Alfred and I were allies, although he was much more restrained in that way. Those good Brevardians never showed offense at my 'holy tone'. And to me that is the way to deal with 'non Christians' of every stripe. Share your faith with them; be polite, personable, but faithful; some of it will rub off. And don't let 'em 'cast you out' the way Alfred wouldn't let 'em.
Alfred could disagree with anyone in the most amiable manner imaginable; he was a walking textbook at that manner, much too unappreciated IMO. When his beloved Quaker wife died after 40 years marriage, Alfred found himself in a retirement center of the Christian Missionary Alliance faith, rabid fundies. He married one of them, a hidebound Republican; after about ten years they seem to get along quite well. PTL.