I would argue that there is an implicit trade-off between bias and decisiveness, similar to trade-offs between accuracy and precision. I take the following to be an unbiased statement.
There may or, equivalently, may not be some manner of supreme being or beings.
I would hold this statement to be relatively non-biased. It is certainly less biased than:
There is a supreme being.
And also less accurate.
I would argue that by not believing in anything you are protected from bias.
Whether it is possible to have no opinions or beliefs is perhaps another question, but I believe by having no opinions to be biased about, it would necessarily result in no bias.
Can you take a position on something as secularly uncertain as say religion or as controversial as social policy and NOT be influenced by feelings or "other limitations" that may make you biased in some form?
Oh no, you asked an extension question about taking a position. Well that makes this harder.
I would argue that being sufficiently informed to produce a position on any issue will necessarily introduce non-zero bias. However, we may be able to further refine our answers. For example, perhaps we can eliminate one of the above cases with the following definition:
A supreme being is taken to be supreme iff superior to all other beings in every way.
then
There may or, equivalently, may not be some manner of supreme being or beings.
reduces to
There may or, equivalently, may not be some manner of supreme being.
Now, should the added definition be considered as a bias? Perhaps, perhaps a clarification, perhaps it is meaningless. These are open questions. However, to me this suggests it is possible to refine statements beyond no position, to some position, to a certain extent, without introduction bias. I would argue that this continues only up to a certain point. To me, religion is beyond that point, but I do believe it may be possible to get down to a single a religion.
I'm tempted to say only time will tell, but I'm worried that may carry with it my internal bias for optimism and progress.