It may be impossible to be totally objective because of so many biases we have. It's very easy to misrepresent, misinterpret, or miss information. We also often look at information through cultural eyes either from a local, regional, social, or national prospective.
If we can do our best to reduce our biases by subjecting ideas to multiple persons using peer review techniques, independent sources, rigorous studies, and skepticism, we can make a very good attempt at representing our knowledge to the best of our ability in order to be objective. Even after doing this, of course, we can still fall victim to our biases and still be wrong [at some point in the future], thus it may be impossible to be absolutely certain about anything... but we can certainly present our best attempts at knowledge and objectivity.
We can't be totally certain about anything, but at some point, we have to stop and make basic assumptions about reality based on evidence we have and trust our well-gained knowledge with good reason. For all we know, we could have came into existence five minutes ago with pre-programmed memories, personalities, feelings and all of our possessions. Since we have no evidence to support claims such as these, we ought not believe them unless the extraordinary evidence did present itself...just like claims of the supernatural.
We can subject supernatural claims to the sword of science and rationality and find that there is no compelling evidence to believe these claims. Extraordinary claims require extraordinary evidence. Millions of things are possible, but if we don't have evidence supporting claims that are extraordinary (or even ordinary), we ought not believe them.
Some claims have much more consequence than others: for example, I don't put too much weight on the claim that your name is Bob. I'll believe it because there is not much consequence in it. If the claim were of much consequence, though, I would not believe and would require more evidence.
There are severe implications for the truth value of Christianity for both theists and atheists. If Christianity is true and Jesus did rise from the dead, believers are in for a treat and the non-believers may not be. The claim that a God exists, performed miracles, created the universe, and sent his son to earth to perform miracles is of great consequence because it challenges and flies in the face of what we now can measure and know about the world. There are great consequences for believing, not believing, and even accepting the claim. the person making this claim is required to produce extraordinary evidence for this claim to be logically acceptable. If the evidence does not exist, we ought not believe it!
The consequence value is not subjective by any means and it is not special pleading. More evidence is needed for claims with more weight, complications, and consequences. The burden, though, still lies with the individual making the claim and not the person who is dismissing it or subjecting it to scrutiny.