>But audience members with opposing views pick up on those inconsistencies and then disbelieve everything the gatekeepers say, even the unbiased truthful stuff.

That's not the fault of the "gatekeepers," nor should it be their problem. Disbelieving everything a source claims because you find "inconsistencies" and "bias" when no human being is ever perfectly consistent or unbiased in their views is an irrational and infantile way of thinking.