The Appeal to Bias fallacy is sometimes employed by a religious apologist to discredit an argument because the person advancing it has a perceived or real bias. It often includes an ad hominin fallacy (attacking the person, not the position).

I have not seen it used often in the wild, but have occasionally run into it.

It is expressed as a syllogism:
Premise 1: X says Y is true (or false).
Premise 2: X is biased.
Conclusion: Y is false (or true).

As an atheist who argues occasionally with religious apologists on the Internet (or as my wife says, “To the keyboard! Someone is wrong on the Internet!” when referring to me), that syllogism might appear as:
Premise 1: James says there is no credible evidence for religious assertions.
Premise 2: James is biased as an atheist.
Conclusion: Religious assertions must be true (because James is an atheist).

The conclusion attacks me, not my claim (there is no credible evidence for religious assertions).

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Headcynic's addendum
You can get more absurdities out of this.

James believes murder is wrong.
James is biased, because he is (liberal, atheist, veteran, etc)
Conclusion: Murder is right.

Walmart sells Coca-Cola
Walmart is biased, because they are a robber-baron capitalist company.
Conclusion: Drinking Coca-Cola means you are a robber-baron capitalist.

(Substitute any other product for Coca-Cola. Broccoli maybe? Donuts? If so, there are a LOT of robber-baron capitalists!)

Hitler liked drapes that touched the floor. (True from various accounts)
Hitler is biased, because he was an evil, murderous tyrant.
Conclusion: Drapes that touch the floor are evil. (I think it's a morally neutral matter of taste.)

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