If there is bias, I would hope it is toward, accepting the sensical, the logical and the evidence-based above the non-sense, the illogical and the opinion-based.
"poppycock", "bull-headed" and "non-sense"
I don't think of the terms "poppycock", "bull-headed" and "non-sense" as being so rude. I would agree that "poppycock" and "bull-headed" are somewhat informal terms. The adjective "non-sense" is definitely not rude. When a claim is non-sense, it must be called non-sense.
We are all humans
Of course, we are all humans, and it is not impossible that some users have been impolite with OPs simply because they don't understand something or because they are opinion based.
If you want to discuss a specific comment/answer that you judge unrespectful, please feel free to open a new metaBiology.SE post to discuss this comment/answer.
Screening for those that can answers
For the vast majority of posts, any user, with any level of reputation can post an answer. Some questions that have already received a lot of unhelpful answers (such as "Me too" or "I love this question, brah!") can be "protected" by some users preventing users that have less than 10 points of reputation to answer.
I noticed that there is some screening process for those allowed to answer questions [..] eliminate the counter argument by controlling the game on an unfair playing field
I am not exactly sure what "screening process" you are referring to here. Can you clarify that? The screening process might be justified in the following section (This is a science website).
This is a science website
Biology.SE is a science website. Hence, only answers that are based upon the method of justification accepted in science (that is evidence are based on observation of the reality) are accepted. An answer based upon, say, a religious book, a vague intuition or some wishful thinking cannot be accepted. In this sense, yes, biology.SE aims at screening answers to select only those that are scientific in nature.
If, for example, a user wants to consider the christian bible as method of justification of knowledge, then please ask your question on Christianity.SE. For other world's major religions, please have a look at islam.SE, hinduism.SE, buddhism.SE or judaism.SE. If a user want to question the validity of different methods of justification of knowledge, please ask over philosophy.SE.