At least in theory. In practice, all but the most liberal evangelicals still maintain a list of pet issues that, although officially regarded as nonessentials, are in practice treated as non-negotiables. Homosexuality is the most obvious example of this double standard; although no mention of it or any related topics appear in the creeds, and although the biblical passages used to condemn homosexuals are all surrounded by significant disputes over context and word translation, many evangelicals who otherwise advocate unity would still break fellowship with any Christian who disagreed with them on this issue alone.
Another issue that remains a hot button among evangelicals is that of biblical inerrancy. Although the exact definition of "inerrancy" remains open to debate, it's nonetheless an issue that conservative Christians largely agree on. Interestingly enough, though, it's not a concept that has much direct biblical support; the closest that the Bible comes to calling itself inerrant is 2 Timothy 3:16-17:
All Scripture is God-breathed and is useful for teaching, rebuking, correcting and training in righteousness, so that the man of God may be thoroughly equipped for every good work.
From that it's a matter of defining and extrapolating from the term "God-breathed" and reasoning that, if God was involved in the process of inspiring the authors of the various books of the Bible, he would have ensured both that what was originally written was free from error of any sort, and that the copies made of those original manuscripts would remain free from all but the most inconsequential of errors.
That still leaves a can of worms to dig through, of course. Are all of the Bible's historical accounts literally factual in the way that we keep historical records today? Should every statement made about God in poetic works like the Psalms be taken at face value as though it came from an encyclopedia, or should the authors be allowed some room for poetic license? Does inerrancy extend to the Septuagint? The manuscripts found among the Dead Sea Scrolls? The King James Version? Does it extend to the books of the New Testament, which hadn't been canonized (and in some cases hadn't yet been written) when Paul made the above statement? What about the books in the Catholic Bible that most Protestants consider apocryphal?
And that's just the tip of the iceberg. Advocates of inerrancy have answers to every objection that's been raised to their position, of course, as well as to those who disagree with them only on particulars, but in the end it's a doctrine that relies more on human reasoning than on anything actually asserted in the Bible. Most evangelicals take inerrancy for granted as a doctrine that's essential to the Christian faith, without ever realizing the irony that a belief system that views human reason as suspect and prone to deception would place so much weight on a doctrine that has its roots in human reason.
For my part, I'm not sure. Archaeological discoveries have repeatedly vindicated the existence of people, places and events mentioned in the Bible. Does that mean that Noah's flood literally covered the entire globe? I don't see why the validity my faith ought to hinge on such matters. Just because God himself does not make mistakes, it doesn't necessarily follow that he micromanages his people to the extent that most versions of inerrancy would require.
Does the Bible have to be completely error-free in the modern sense of the term to be a reliable foundation for the Christian faith? Can it still be "God-breathed and useful for teaching, rebuking, correcting and training in righteousness" even if Genesis 1-3 doesn't provide a C-SPAN-style transcript of how God brought the world and its first inhabitants into existence?
I run the risk of conflating two separate debates here, since not all inerrantists require that the early chapters of Genesis be taken completely literally, but many of them do. One of the core concerns of inerrantists is that if the Bible is found to contain even the slightest error (or anything that could be considered 'fiction' by the modern definition), then all of it must be regarded as equally unreliable. Although that's not how the real world works, it's a very real fear in the minds of those who require absolute certainty.
I'm not ready to discard the doctrine of inerrancy, since I do see validity in some of its claims, but neither do I see it as an essential doctrine that should be used to draw the line between "true believers" and "heretics." While I understand the fears of those who advocate strongly for inerrancy (and those fears aren't completely baseless), I've also come to see how a need for absolute certainty, far from being a component of a healthy spiritual life, is in fact a sign of a weak and immature faith.
For my part, I'm willing to live with a healthy dose of uncertainty. It may not always make for a comfortable life, but when did God ever promise us one of those?