How can a Christian reject part of the Bible and still call themselves a Christian?

[Lek]

I am still open, but my openness is now tempered with a lot more knowledge.

For example, I understand how easy the human mind can be fooled. Even the most sane people are susceptible to: hallucination, confirmation bias, misinterpretations of sensory input, misinterpretation of nonstandard natural brain states, etc.

So, if a god does exist, and it wants to convince me of its existence, it would know exactly how to do so, without resembling any of the above possible natural explanations. If, on the other hand, said god communicates with me without me being able to differentiate it from a natural explanation, then how is it my fault for not being convinced?

I hear and understand what you are saying.   If God was to speak to you now, you would then believe in him and follow him.  Since you are still open, I assume you feel it would actually be God speaking to you and not one of those things you mentioned above, to which you are susceptible as a human being.  This would be because God has the power to make himself clear when he speaks to you despite these other human tendencies.  And I'm not putting blame on you, rather I'm just relating the way I understand it to be.