Just to clarify … I don't think anyone would suggest that the lists of Fundamentalism's fundamentals, in Part 2, are in some way authoritative, nor encyclopedic of Christian teaching. The lists are, however, historically interesting and a reasonable reference point for thought. Another such reference point I will be using will be the passage quoted in Part 2 from Hebrews 6.
Common to both lists is the unique inspiration and authority of Scripture. This, of course, derives from what Scripture says of itself (2 Timothy 3:16-17), primarily, and secondarily from church history. Without Scripture – all of Scripture, not just what suits my fancy (which then would make me the source of authority) – Christianity could be whatever each and every person chooses to say it is (“I think Christianity is a ham-on-rye sandwich. Prove me wrong!”). If Christianity is anything and everything anybody and everybody says it is, it is reduced to meaningless nothingness. Scripture, then is the measuring device, the level, the plumb line – the standard for and source of Christian teaching. Scripture, and acceptance thereof, is a boundary defining what is and isn't Christian teaching.
What does this mean in practical terms for Christian fellowship? Well, as I posted previously, I have neither the authority nor the knowledge to say whether or not a person is truly a Christian believer. So, in principle, it is possible for some one to be unaware of or not accept the full authority of the Bible and yet be a Christian believer. That said, realistically, a person who rejects the full authority of the Bible and approaches it like a buffet table – picking what they like while leaving the rest – is unlikely to “like”, to accept, the message that they are a sinner and in need of a Savior. And such a person is also likely to find unpalatable much that the Bible (including the teachings of Jesus) identify as morally right or wrong. So the basis for fellowship with such persons is will, at best, be tenuous (thus, automatic rejection would be wrong), and very possibly non-existent. A person unaware of the authority of Scripture and says they are a Christian believer will, in a fellowship or service situation, soon be faced with choices about the authority of Scripture. Scripture challenges every person by providing an honest view of what that person is. And the bases for Christian fellowship will come out of those choices – whether acceptance, rejection or compromise.