While Bible-believing Christians may disagree on how to interpret Genesis 1 and 2, they all hold to the following three essentials.
First, they believe the Bible, including Genesis, to be the infallible repository of redemptive revelation. They may differ on interpretation but never on inspiration.
Furthermore, they are committed to the truth that God created the universe out of nothing at all (creatio ex nihilo). Moreover, they hold to horizontal changes within living kinds (microevolution*, as when bacteria becomes resistant to antibiotics), but never vertical changes from one kind to another kind (macroevolution*).
Finally, they hold Adam and Eve to be special creations made in the image of God rather than fictional exemplars of primitive humanity. As such, they deny naturalistic paradigms—including a version of theistic evolution in which God is said to have employed purely natural processes to produce the first humans.
If such naturalistic paradigms are true, Genesis is at best an allegory and at worst a farce. And if Genesis is either an allegory or a farce, the rest of the Bible is utterly irrelevant. In other words, if Adam and Eve did not eat the forbidden fruit and fall into a life of perpetual sin terminated by death, there is no need for redemption.
the world, and all who live in it;
for he founded it upon the seas
and established it upon the waters.
For further study, see The Genesis Debate: Three Views on the Days of Creation, ed. David G. Hagopian (Mission Viejo, CA: Crux Press, 2001).