Biblical Inerrancy - mandatory to be Christian?

[Silver]

5. If all morals are equally false, a state of nihilism is reached where people have no obligation to obey any morals. (EF = nihilism)

I feel like focusing on this particular section, both because of how false it is and because it unnerves me that Christians believe they would do evil things if their god was proven to not exist. How ever would they know right from wrong without a god to guide them? If one cannot use common sense to know right from wrong without a deity to hold his hand, then that individual is a sociopath who obviously lacks the moral compass inherently built into all of us. One should know that he should do good for the sake of doing good, not because a higher authority states it must be so.